{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":56593,"title":"List the nth term of Rozhenko’s inventory sequence","description":"Consider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\r\n0\r\n1, 1, 0\r\n2, 2, 2, 0\r\n3, 2, 4, 1, 1, 0\r\n4, 4, 4, 1, 4, 0\r\nWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19th term is 4. \r\nThis sequence produces interesting plots and music. See the related Numberphile video for more. \r\nWrite a function to report the th term of this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 345px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 172.5px; transform-origin: 407px 172.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.6px 8px; transform-origin: 374.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1, 1, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.2167px 8px; transform-origin: 27.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2, 2, 2, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3, 2, 4, 1, 1, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4, 4, 4, 1, 4, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e term is 4. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.425px 8px; transform-origin: 112.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis sequence produces interesting \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A342585/graph\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eplots\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/play?seq=A342585\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003emusic\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 8px; transform-origin: 18.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. See \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=rBU9E-ZOZAI\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ethe related Numberphile video\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.8833px 8px; transform-origin: 31.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for more. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.1px 8px; transform-origin: 90.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to report the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5583px 8px; transform-origin: 78.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Rozhenko(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 19;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny_correct = 5;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 347;\r\ny_correct = 25;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 823;\r\ny_correct = 27;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 1997;\r\ny_correct = 20;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 4721;\r\ny_correct = 68;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 13859;\r\ny_correct = 18;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 19793;\r\ny_correct = 7;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 24677;\r\ny_correct = 51;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 41903;\r\ny_correct = 357;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 25537;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(Rozhenko(Rozhenko(n))),y_correct))\r\n\r\n%%\r\nn = [1 4 8 14 20 28 37 46 57 69 82 95 110 125 142 159 177 196 216 238 260 285 310 335 362 390 418 448 478 511];\r\na = arrayfun(@Rozhenko,n);\r\ns_correct = 0;\r\nassert(isequal(sum(a),s_correct))\r\n\r\n%%\r\nfiletext = fileread('Rozhenko.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-11-13T14:07:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-13T04:07:55.000Z","updated_at":"2026-01-24T12:19:36.000Z","published_at":"2022-11-13T04:08:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1, 1, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2, 2, 2, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3, 2, 4, 1, 1, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4, 4, 4, 1, 4, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e term is 4. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis sequence produces interesting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A342585/graph\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eplots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/play?seq=A342585\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emusic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. See \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=rBU9E-ZOZAI\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe related Numberphile video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to report the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term of this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50948,"title":"Identify prime words","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6083px 7.91667px; transform-origin: 13.6083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=9CcI5M1LfRs\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eNumberphile video on evil primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 236.375px 7.91667px; transform-origin: 236.375px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, Tony Padilla introduced the “Jesus prime” 105,192,119, which is formed by concatenating the positions of the letters of ‘Jesus’ in the English alphabet: 10, 5, 19, 21, 19. In general, a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.625px 7.91667px; transform-origin: 34.625px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eprime word\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.91667px; transform-origin: 20.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e could be defined as a word such that the number formed by concatenating the positions of the letters in the alphabet is prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.425px 7.91667px; transform-origin: 368.425px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a string and identifies prime words. It should delete apostrophes and hyphens (e.g. “don’t” = “dont”, “un-ionized” = “unionized”) and treat other punctuation as spaces. The function should return an array of 0’s and 1’s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isPrimeWord(s)\r\n  tf = isprime(s);\r\nend","test_suite":"%%\r\nassert(isPrimeWord('Croatia'))\r\n\r\n%%\r\nassert(~isPrimeWord('Serbia'))\r\n\r\n%%\r\nassert(isPrimeWord('frenetic'))\r\n\r\n%%\r\nassert(~isPrimeWord('frantic'))\r\n\r\n%%\r\nassert(isPrimeWord('smiling'))\r\n\r\n%%\r\nassert(~isPrimeWord('frowning'))\r\n\r\n%%\r\nassert(isPrimeWord('ziti'))\r\n\r\n%%\r\nassert(~isPrimeWord('spaghetti'))\r\n\r\n%%\r\nassert(isPrimeWord('tick'))\r\n\r\n%%\r\nassert(~isPrimeWord('tock'))\r\n\r\n%%\r\nassert(isPrimeWord('madam'))\r\n\r\n%%\r\nassert(~isPrimeWord('Adam'))  \r\n\r\n%%\r\nassert(isPrimeWord('RFQ'))\r\n\r\n%%\r\nassert(~isPrimeWord('FAQ'))\r\n\r\n%%\r\nassert(isPrimeWord('Jesus'))\r\n\r\n%%\r\nassert(~isPrimeWord('Moses'))  \r\n\r\n%%\r\nassert(isPrimeWord('adieu'))\r\n\r\n%%\r\nassert(~isPrimeWord('milieu'))\r\n\r\n%%\r\nassert(isPrimeWord('wallow'))\r\n\r\n%%\r\nassert(~isPrimeWord('swallow'))  \r\n\r\n%%\r\ns = 'slim pickings';\r\nassert(all(isPrimeWord(s)))\r\n\r\n%%\r\ns = 'mellow fellow';\r\nassert(all(isPrimeWord(s)))\r\n\r\n%%\r\ns = 'Ms. Zadora stuck a cornucopia full of Bing cherries into her knapsack.';\r\ntf_correct = [1 1 1 0 1 0 0 1 0 0 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%%\r\ns = 'The dog and pig are going to India.';\r\ntf_correct = [0 1 0 1 0 1 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%%\r\ns = 'Liam, is Mauritius in Africa? I know that Mali and Libya are.';\r\ntf_correct = [1 1 1 0 1 0 0 0 1 0 1 0];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%% Maria Bamford\r\nq = char(39);\r\ns = ['I was in a lot of plays. We had a weird drama teacher in that he was incredibly enthusiastic about a high school drama program and would talk to all the kids for hours. He ended up marrying one of the kids, but that' q 's neither here nor there.'];\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[28 32 42]))\r\n\r\n%% Maria Bamford\r\nq = char(39);\r\ns = ['I do wanna get married. It just sounds great. You get to go grocery shopping together, rent videos, and the kissing and the hugging and the kissing and the hugging under the cozy covers. Mmmm! But sometimes I worry that I don' q 't wanna get married as much as I want to get dipped in a vat of warm, rising bread dough. That might feel pretty good, too.'];\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[3 15 34 43]))\r\n\r\n%% Monty Python\r\ns = 'I cut down trees, I eat my lunch, I go to the lavatory. On Wednesday I go shopping and have buttered scones for tea.';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[4 18]))\r\n\r\n%% Monty Python\r\ns = 'Strange women lying in ponds, distributing swords, is no basis for a system of government!';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[8 10]))\r\n\r\n%% Monty Python\r\ns = 'My hovercraft is full of eels.';\r\ntf_correct = [0 0 1 0 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n    \r\n%% Basil Fawlty\r\ns = 'Well may I ask what you expected to see out of a Torquay hotel bedroom window? Sydney Opera House perhaps? The Hanging Gardens of Babylon? Herds of wildebeest sweeping majestically';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[18 23]))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-03-14T22:44:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-14T16:24:34.000Z","updated_at":"2026-01-20T19:15:07.000Z","published_at":"2021-03-14T16:29:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=9CcI5M1LfRs\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNumberphile video on evil primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, Tony Padilla introduced the “Jesus prime” 105,192,119, which is formed by concatenating the positions of the letters of ‘Jesus’ in the English alphabet: 10, 5, 19, 21, 19. In general, a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprime word\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e could be defined as a word such that the number formed by concatenating the positions of the letters in the alphabet is prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a string and identifies prime words. It should delete apostrophes and hyphens (e.g. “don’t” = “dont”, “un-ionized” = “unionized”) and treat other punctuation as spaces. The function should return an array of 0’s and 1’s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57447,"title":"Compute a nested cube root","description":"Consider the quantity . Write a function to compute  without using loops or recursion. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.075px 8px; transform-origin: 68.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the quantity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\" style=\"width: 249px; height: 19.5px;\" width=\"249\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.875px 8px; transform-origin: 90.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Write a function to compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.575px 8px; transform-origin: 71.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e without using loops or recursion. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = nestedCubeRoot(a)\r\n  y = nthroot(a+nthroot(a+nthroot(a+nthroot(a,3),3),3),3);\r\nend","test_suite":"%%\r\na = 6;\r\nassert(abs(nestedCubeRoot(a)-2)\u003c1e-14)\r\n\r\n%%\r\na = 24;\r\nassert(abs(nestedCubeRoot(a)-3)\u003c1e-14)\r\n\r\n%%\r\na = 120;\r\nassert(abs(nestedCubeRoot(a)-5)\u003c1e-14)\r\n\r\n%%\r\na = 336;\r\nassert(abs(nestedCubeRoot(a)-7)\u003c1e-14)\r\n\r\n%%\r\na = 1320;\r\nassert(abs(nestedCubeRoot(a)-11)\u003c1e-14)\r\n\r\n%%\r\na = 15/8;\r\nassert(abs(nestedCubeRoot(a)-3/2)\u003c1e-14)\r\n\r\n%%\r\na = 2040/2197;\r\nassert(abs(nestedCubeRoot(a)-17/13)\u003c1e-14)\r\n\r\n%%\r\na = 9048/12167;\r\nassert(abs(nestedCubeRoot(a)-29/23)\u003c1e-14)\r\n\r\n%%\r\na = 29520/29791;\r\nassert(abs(nestedCubeRoot(a)-41/31)\u003c1e-14)\r\n\r\n%%\r\na = 117384/226981;\r\nassert(abs(nestedCubeRoot(a)-73/61)\u003c1e-14)\r\n\r\n%%\r\na = 2259912/3869893;\r\nassert(abs(nestedCubeRoot(a)-191/157)\u003c1e-14)\r\n\r\n%%\r\nfiletext = fileread('nestedCubeRoot.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'switch') || contains(filetext,'for') || contains(filetext,'while') || length(strfind(filetext,'nestedCubeRoot')) \u003e 1;\r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-21T13:18:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-21T13:13:13.000Z","updated_at":"2026-03-04T12:08:30.000Z","published_at":"2022-12-21T13:18:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = (a+(a+(a+(a+\\\\ldots)^{1/3})^{1/3})^{1/3})^{1/3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Write a function to compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e without using loops or recursion. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58946,"title":"Count block fountains","description":"A block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \r\nWrite a function to compute the number of block fountains with  circles on the first row. For example, there are five block fountains with three circles on the first row. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 429.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 214.85px; transform-origin: 407px 214.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 364.85px 8px; transform-origin: 364.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.125px 8px; transform-origin: 195.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the number of block fountains with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.958px 8px; transform-origin: 176.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e circles on the first row. For example, there are five block fountains with three circles on the first row. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 327.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 163.85px; text-align: left; transform-origin: 384px 163.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"543\" height=\"322\" style=\"vertical-align: baseline;width: 543px;height: 322px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = blockFountain(n)\r\n  y = factorial(n);\r\nend","test_suite":"%%\r\nassert(isequal(blockFountain(3),5))\r\n\r\n%%\r\nassert(isequal(blockFountain(5),34))\r\n\r\n%%\r\nassert(isequal(blockFountain(8),610))\r\n\r\n%%\r\nassert(isequal(blockFountain(14),196418))\r\n\r\n%%\r\nassert(isequal(blockFountain(14),196418))\r\n\r\n%%\r\nassert(isequal(blockFountain(23),1134903170))\r\n\r\n%%\r\nassert(isequal(blockFountain(28),139583862445))\r\n\r\n%%\r\nassert(isequal(blockFountain(33),17167680177565))\r\n\r\n%%\r\nassert(isequal(blockFountain(35),117669030460994))\r\n\r\n%%\r\nfiletext = fileread('blockFountain.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-03T17:54:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2023-09-03T17:54:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-02T14:47:44.000Z","updated_at":"2026-01-26T19:21:38.000Z","published_at":"2023-09-02T14:47:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the number of block fountains with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e circles on the first row. For example, there are five block fountains with three circles on the first row. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"322\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"543\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46003,"title":"Compute Khinchin's constant","description":"Khinchin's constant K_0 = 2.684542001... (also written \"Khintchine's constant\") has the amazing property that it is the limiting value of the geometric mean of the partial quotients from a continued fraction expansion of almost all numbers. In other words, if a number x is expanded as \r\n\r\n\u003c\u003chttps://wikimedia.org/api/rest_v1/media/math/render/svg/d60c339a507116862b2c43d6d447db411c4277d3\u003e\u003e\r\n\r\nthen \r\n\r\n\u003c\u003chttps://wikimedia.org/api/rest_v1/media/math/render/svg/8a05ee602e42ba03dcfa068f518a0664eebc3bc0\u003e\u003e\r\n\r\nMore information is available at \u003chttps://en.wikipedia.org/wiki/Khinchin%27s_constant Wikipedia\u003e, \u003chttps://mathworld.wolfram.com/KhinchinsConstant.html Wolfram MathWorld\u003e, the \u003chttps://oeis.org/A002210 Online Encyclopedia of Integer Sequences\u003e, and \u003chttps://www.youtube.com/watch?v=VDD6FDhKCYA Numberphile\u003e. \r\n\r\nCompute Khinchin's constant. The test suite will check for a difference of 10^{-12}. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 298.833px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 149.417px; transform-origin: 407px 149.417px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.6333px; text-align: left; transform-origin: 384px 31.6333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.0167px 7.91667px; transform-origin: 62.0167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eKhinchin's constant \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAoCAYAAACWwljjAAABhUlEQVRYhe2WXZGEMBCEPw84wAAGULAKcHAO1gEW0IAEPGABDVi4ewhTdFLh53YhvKSreCAZkmZ6phPIyMh4FjXw3nl+JHYvrriSVAG0wK88E1BGYhuJmRcyt6AOCMXIAHSshKu7yICTxsgMB2QGLpYohkEIhTIUQL8xdxtUrlrGK2DE1csrFZkXfqGaHCbjRAKJFNphPb5EXUoihlEIdbiMzPgelAwFfv0c+dDtCI1ukvf2CULmLSaXGuTMA1nSjDTLmHpSf3KdAvdD9gx84OQVft2UG+NHCxe4bFqHwmoZ/yKlx8UUzKmU48E6FlsH4/OJbz2Y18QKuFwWtPktl9YuDc3TpA+JbkJliW34xs9gzK2tCWKZsO9PdWt43YhtZrVhMTGjtE33CG3dHjzocbGns8bFbOAMocM6qvH/fCbeDXqm6V1JY78m1LB9L25OxmmsdepXGboSlxX1lTA5Q1jbJ7vYGfaMMfnlDlZ70Pa22kqeHUPJeqi2uO487dAZGRkZKfEHkq692W7XbbgAAAAASUVORK5CYII=\" alt=\"K_0\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 312.983px 7.91667px; transform-origin: 312.983px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 2.684542001... (also written \"Khintchine's constant\") has the amazing property that it is the limiting value of the geometric mean of the partial quotients from a continued fraction expansion of almost all numbers. In other words, if a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.0167px 7.91667px; transform-origin: 49.0167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is expanded as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.6667px; text-align: left; transform-origin: 384px 42.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.91667px; transform-origin: 13.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-69px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUEAAACrCAYAAAD4pi5hAAAJ7klEQVR4nO3dvZXjOBqF4ZvCHFrr0m1DAawiUAS01mxlILsdpaAYFIJykDsmY1AKWgP6GiALpEiK4h/e5xycmSmqVVTX8NZHAAQkAAAAAAAAAAAAAAAAfCaTdJz7JABgapmkk6THqwFAMo5ywfd8NUIQQDKOkvZylWApQhBAwm4iBAEkjBAEkDRCEEDSCEGgg9Or5XOfCEZHCAId2DSK3dwngtERgkAHhOB2EYJAB4TgdhGCG5BLKiRd5H6g+9rx4vX1y8Tn9Sl7nvMqd/7WJ3dS/HN+EyG4XYTgyh0kneWCwS7UW3D8Enz9qW4d+7vXe3zaig8+lz3SdJUPnkLVx5yyD96/L0JwuwjBDQkDz6qo2+vfC3VfJWOvanAObUNX5bDPcY0ciwX9FAjB7SIEN6RQNYDuGjalI5MLwk/bkErNArAp5OzznQa89ycIwe0iBDckV7USm7LPbAx2S/9QPLx3eh9GOw0L4LPab+3DCrStYX0IwY2xFTHuc59IT2GAnxtec3wdL/Uz5Pavr5/kKuJS/W7Hw6Ab2riI1okQ3Bi7nSznPpGe7LybqkDJB3y9r9AqxDA8rV+z6+CMVZBNLexmaHoNt8rrdBchuBm5qqOnQy/KqUeHs+CcY4Mh0s/+zpD9Jq9/3lLxqnEI+gS3x6ZbhdX8SdPOOsDI7qqOEA8dnZ16dPjw5s+EC1/Wp/mEt9F1V/WrBtsQgtuyl38ePNYO850ahjrLV1Gx28aduv+Gm3p0OPxtHPuf7yJ/y2KVXSYXgBagsT5Qe9+mPsY+CEFgwQpVp8OE/WuSv71daplvAx6xqu0i/8SIBXsm93kL+aBrC8ExBokIQWBBrO/Pnqh4qHpxhv1nF7nqacnTZcJb2lKuujvIBZ9Vs+EUlbv8bTMhCCQonC/30M+Ay+QHSGLHlyisBi0Mw/7BcDOc8OuEIJCoXO39btmb40tk5xwLGjtWZ1VvWwiOMYmZEASwSFYVx0LwrHkesQOASdmtf73qtcGUJXUH/KLRaJ0bOrLb3nBk2SZg32c5o7h/NM78SxotlfZb6Oyun9OE2h7Bm8sfGo3WuaEnW137LDeCvKZBIQAAAAAAAADAtuVyfdhMwAeQFAs/mwZCCAJIQiY3p/Wu6lw4QhBAEsJn+e2RTkIQQJLChYQJQQDJIQQBJI0QBJA0QhBA0ghBAEkjBIEFs713l7YM2ZYQgsCCcXF+HyEILBgX5/cRgsCCcXF+HyEI1GRyq2Ff5TaIsj650+u/p9wsiovz+whBIHCU2w/lKn9BFPK76D017VYBXJzfRwgCL7ak0jVyzC6SMTaP74OL8/sIQUA+AJtCzi6SqTeP5+L8PkIQybOLoGlb0J26XSR5w59vc5YL3qYWVqBtDcOFi6pO2d8LLEIufwGcG15zfB0vFe8PzOTXpDv0/P5h0A1tj57fE+5ndlA1AJ9yi6wWIgyRELsI2jaHL9XcV3iUqyRt4KRvCO7kLrimZhfnseU13ML1l6n9752/UyQhkw+ZWMBJrioIg6iJVXR9Q/Ad+qoAfM1B7QGXyVeBT7X39xGCAFYnHBWMhddFfiMe6w/MFA9DQhDA6tiAx1Putjd0kX9ixG6XM/mO8zpCEMDqhCPDpVyAHeQCzfoIwykqdzX3CxKCAFYprAYtDMOgsz7BhxgYAbBRNl0iFjR27J2lh+AfGu3DBrT6VgiO4Zc+n5BNo/0W0GLJISi5IKTRPmlAq6WHIAB8lQ2gxKbPAMBm7VRdCeYiVw1OufAqAAAAgDXJ5Z9MAoBkWPjZ1BNCEEAyjvLVHyEIIDnhCkSEIICkEYIAkkYIAkgaIQggaYQggKQRggCSRggCSBohCCBphCCAv3K5LVBPc5/IhAhBAH/t5QLhMfeJTIgQBPAXIQggaYQggFlYX5ytjF2oulr2VCtkE4IAJpXJBd3z9U8Lu4tcED0l3Sc8H0IQwGQyuYB7yq1vF7IwemrakdrUQjD8e57ylw2QvDAAYyEXXpz7Cc8rlRAsVF1Q1Vop9/PYzXdqQBpsf+Sm6uMof1HG+gMzucAaEpC3lmbB/HjzuvOA7wsAklwVYpVH0ybxVqXU+6ky+QANq5c+m83Xq58hjf4zAIPZBvFNVWAuHzb1vsK73O1apupGQQ91v4XbtzSrQJ9vXpf/eFcA6OCg5oAz4Q5oYbAdFK/A2voW+0qlTxDATGw6TD3gzC44XtaOFYpXYCf5KTafIgQBfFXYn1cf8LD+Prtdtqovj7w2ZCFYjHB+hCCArwqnZYRVnU2ZCfvkjnKVYan2/j57zzGeKiEEAXxVODJ8kwudQi7ojqrOD7y8vt42DSaTC6yxJlSPFYL/kfQv7Svtvz1+DsAi1Sfp3uSnuIQjw+8CUHLhN+aTDoTg8hshiE3I1TzVJFe36S52qzzm4grcDgNYBbsNZr4egOTYIErTFBsA2CwLwNh0mGPD1wFgM26KL25wF/14a9Q0AR5ARKH2lV2aHsPD8ti0qKYnhwBgk/by4df2+CQAbM7h1TJV54oSggCSY897E4IAkkQIAkgaIQggaYQggKQRggCSRggCSBohCCBphCCApBGCAJJGCAJIGiEIYHa5XBiNtUlVH4QggNnNuZ8KIQhgdoQggKTNGYJnEYJAsqwvzlbELuSC4Pz67zG3EG0zRwhmcp/3IR+CV7HEPpCETL4COsuH3UU+FMbcSP6dqUMwHIiJNbZHADbMdsl76ufFbmH01LQjtWw0D2ASYQDGQi4Mwf2E50UIApjETe23usfX8VLx/sBMLrD2Dcfffe+mZsEc28I0bOee3xMA/irkq7xDw2ts06Fr5Fg4impB2adafI7QYucFAJ3Y9pJNVWAuHzb1vkIbQbaRU6sY7+peEe5bmr3f883rGLkFMMhBzQFnLsFrwvlymVwA1tkt7BjTaOgTBPBV7yYE74LjZcf3tL68MYwZgr8mbABWwgZEYpWbVXp2u2z9bnnktQqOjfmExVgh+D+N0/fYtf3+8HwBTMQGPJ6q9qvZlJmwT+4oF26lmqvGu9zt81h9dGNWgn8mbABWIhwZvsmFTiEXdEdV5wde1Dzye5TvC7T3ok8QwCqE1aAFmE2VCUeGu0x92cs/Xtc03aYPQhDAJHI1TzXJ1a+Pz4JrjAnMhCCAVRorBAFglca6HQaARYvdJttafACwadZfV8pXfXs1T6EBgE3JVF19+iJXBQIAVmQvF+ZTrpMIAIsQTgZ/iCAEkJhwW822lXQAYJNy+SdcHppuFz0AWAzbGgAAAABwbA9ipv0ASE4m31fIgAmA5IRTZ9jNDkCSwkViGTgBkKQhm8kDAAAAALBBO7mBkqtYMgxAgmwf5qfG22QeAFYjnD9YznwuADA52z7gIfZRAQAAAAAAAAAAAAAAAAAAAJCq/wMPp29XjxShfgAAAABJRU5ErkJggg==\" alt=\"Continued fraction expansion of x\" style=\"width: 160.5px; height: 85.5px;\" width=\"160.5\" height=\"85.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.9px 7.91667px; transform-origin: 24.9px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n approaches infinity\" style=\"width: 46.5px; height: 18px;\" width=\"46.5\" height=\"18\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.6333px; text-align: left; transform-origin: 384px 10.6333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.91667px; transform-origin: 13.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K_0 is the nth root of the product of a_1 through a_n\" style=\"width: 133.5px; height: 21px;\" width=\"133.5\" height=\"21\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.8667px 7.91667px; transform-origin: 96.8667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMore information is available at\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Khinchin%27s_constant\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/KhinchinsConstant.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWolfram MathWorld\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6167px 7.91667px; transform-origin: 13.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A002210\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOnline Encyclopedia of Integer Sequences\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5667px 7.91667px; transform-origin: 15.5667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=VDD6FDhKCYA\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 39.7px 7.91667px; transform-origin: 39.7px 7.91667px; \"\u003eNumberphile\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.417px 7.91667px; transform-origin: 226.417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute Khinchin's constant. The test suite will check for a difference of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"10^{-12}\" style=\"width: 35px; height: 19.5px;\" width=\"35\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function K0 = KhinchinsConstant\r\n  K0 = ...;\r\nend","test_suite":"%%\r\nassert(abs(KhinchinsConstant-2.68545200106530644)\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('KhinchinsConstant.m');\r\nx = ~isempty(strfind(filetext, 'A002210')) || ~isempty(strfind(filetext, '2.68545200106')) ||...\r\n    ~isempty(strfind(filetext, 'char')) || ~isempty(strfind(filetext,'str2num')) ||...\r\n    ~isempty(strfind(filetext, 'urlread'));\r\nassert(~x, 'Illegal approach. Try one of the formulas on the Wolfram MathWorld page.')","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-30T04:17:42.000Z","updated_at":"2026-01-24T11:49:57.000Z","published_at":"2020-06-30T05:17:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eKhinchin's constant \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K_0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 2.684542001... (also written \\\"Khintchine's constant\\\") has the amazing property that it is the limiting value of the geometric mean of the partial quotients from a continued fraction expansion of almost all numbers. In other words, if a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is expanded as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Continued fraction expansion of x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = a_0+\\\\frac{1}{a_1+\\\\frac{1}{a_2+\\\\frac{1}{a_3 + \\\\frac{1}{\\\\ddots}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n approaches infinity\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\\\\to\\\\infty\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K_0 is the nth root of the product of a_1 through a_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_0 = (a_1a_2a_3\\\\ldots a_n)^{1/n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore information is available at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Khinchin%27s_constant\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/KhinchinsConstant.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWolfram MathWorld\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A002210\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOnline Encyclopedia of Integer Sequences\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=VDD6FDhKCYA\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNumberphile\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute Khinchin's constant. The test suite will check for a difference of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"10^{-12}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10^{-12}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51975,"title":"Compute a sum of Ramanujan","description":"Srinivasa Ramanujan defined the following function:\r\n\r\nWrite a function to compute  for various values of . See also Cody Problems 45960 and 46000.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 160.675px 7.79167px; transform-origin: 160.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSrinivasa Ramanujan defined the following function:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"phi(a) = 1+2 Sum[1/((a k)^3 - a k),{k,1,infinity}]\" style=\"width: 162.5px; height: 45px;\" width=\"162.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.9917px 7.79167px; transform-origin: 86.9917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"phi(a)\" style=\"width: 32.5px; height: 18.5px;\" width=\"32.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.5083px 7.79167px; transform-origin: 66.5083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for various values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.85px 7.79167px; transform-origin: 82.85px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. See also Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45960\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e45960\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e46000\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Ramanujanphi(a)\r\n  y = f(a);\r\nend","test_suite":"%%\r\na = 2;\r\ny_correct = 2*log(2);\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 3;\r\ny_correct = log(3);\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 4;\r\ny_correct = (3/2)*log(2);\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 5;\r\nphi = (1+sqrt(5))/2;\r\ny_correct = (sqrt(5)/5)*log(phi)+(1/2)*log(5);\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 6;\r\ny_correct = (1/2)*log(3)+(2/3)*log(2);\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 7;\r\ny_correct = (2/7)*(log(14)+2*cos(pi/7)*log(cos(pi/14))+2*log(cos(3*pi/14))*sin(pi/14)-2*log(sin(pi/7))*sin(3*pi/14));\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 8;\r\ny_correct = log(2)+(sqrt(2)/8)*log((2+sqrt(2))/(2-sqrt(2)));\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 12;\r\ny_correct = (1/2)*log(2)+(1/4)*log(3)+(sqrt(3)/6)*log((sqrt(3)+1)/(sqrt(3)-1));\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 18;\r\nb = pi/9;\r\ny_correct = (1/9)*(log(2)+2*log(6)+log(sqrt(3)/2)+2*cos(b)*log(cos(b/2))+2*cos(2*b)*log(cos(b))-2*cos(b)*log(sin(b/2))-2*cos(2*b)*log(sin(b))+2*log(cos(2*b))*sin(b/2)-2*log(sin(2*b))*sin(b/2));\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = [11 13 17];\r\nsum_correct = 3.003409919427940;\r\nassert(abs(sum(Ramanujanphi(a))-sum_correct)\u003c1e-14)\r\n\r\n%%\r\na = [36 54 72 100];\r\ny_correct = [1.0000515628258977 1.0000152722224909 1.0000064421348023 1.000002404321212];\r\nk = randi(4);\r\nassert(abs(Ramanujanphi(a(k))-y_correct(k))\u003c1e-14)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2021-06-05T14:29:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-05T14:22:18.000Z","updated_at":"2026-01-20T21:12:40.000Z","published_at":"2021-06-05T14:23:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSrinivasa Ramanujan defined the following function:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phi(a) = 1+2 Sum[1/((a k)^3 - a k),{k,1,infinity}]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\phi(a) = 1+2\\\\sum_{k=1}^\\\\infty\\\\frac{1}{(a k)^3 – a k}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phi(a)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\phi(a)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for various values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. See also Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45960\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45960\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e46000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60456,"title":"Compute a sum","description":"Write a function to compute the following sum\r\n\r\nAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 126px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 63px; transform-origin: 407px 63px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.067px 8px; transform-origin: 141.067px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following sum\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"123.5\" height=\"45\" alt=\"S = Sum[(an+b) u^n/(n*(n+m)*v^n),{n,1,Infinity}]\" style=\"width: 123.5px; height: 45px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.108px 8px; transform-origin: 375.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = JPMsum1(a,b,m,u,v)\r\n  y = sum([v u m b a]);\r\nend","test_suite":"%%\r\na = 4;\r\nb = 9;\r\nm = 1; \r\nu = 5;\r\nv = 9;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 7;\r\nb = 32;\r\nm = 2; \r\nu = 3;\r\nv = 4;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 16.5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 168;\r\nb = 1058;\r\nm = 2; \r\nu = 19;\r\nv = 23;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 617.5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 19;\r\nb = 81;\r\nm = 3; \r\nu = 2;\r\nv = 3;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 80/3;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 547;\r\nb = 8232;\r\nm = 3; \r\nu = 13;\r\nv = 14;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 13390/3;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 6095;\r\nb = 82944;\r\nm = 4; \r\nu = 11;\r\nv = 12;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 36704.25;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 469711;\r\nb = 9447840;\r\nm = 5; \r\nu = 17;\r\nv = 18;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 3817735.9;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 117585;\r\nb = 705894;\r\nm = 6; \r\nu = 2;\r\nv = 7;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 593732/15;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\nfiletext = fileread('JPMsum1.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'switch') || contains(filetext, 'if'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-09T16:09:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2024-06-09T16:09:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-09T02:41:38.000Z","updated_at":"2026-02-01T07:00:29.000Z","published_at":"2024-06-09T02:41:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following sum\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S = Sum[(an+b) u^n/(n*(n+m)*v^n),{n,1,Infinity}]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS = \\\\sum_{n = 1}^\\\\infty \\\\frac{an+b}{n(n+m)} \\\\frac{u^n}{v^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58394,"title":"Integrate a product of gamma functions","description":"Write a function to compute the following integral:\r\n\r\nwhere  and  is the gamma function, the subject of Cody Problem 46025.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.05px; transform-origin: 407px 52.05px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 8px; transform-origin: 152.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 196.5px; height: 44px;\" width=\"196.5\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.55px; text-align: left; transform-origin: 384px 10.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 56px; height: 20px;\" width=\"56\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.842px 8px; transform-origin: 117.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gamma function, the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46025\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46025\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = intGammaProduct(a)\r\n  f = @(x) gamma(1+i*a*x)*gamma(1-i*a*x);\r\n  y = trapz(x,f);\r\nend","test_suite":"%%\r\na = tan(1);\r\nI_correct = 1.008596722571773;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sqrt(2);\r\nI_correct = 1.110720734539592;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = log(3);\r\nI_correct = 1.429800433690064;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = exp(4);\r\nI_correct = 0.028770138289325;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sinh(5);\r\nI_correct = 0.021168845856719;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = asinh(6);\r\nI_correct = 0.630391294450658;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-06-03T19:50:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-03T14:18:04.000Z","updated_at":"2026-01-26T04:29:04.000Z","published_at":"2023-06-03T14:18:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_{-\\\\infty}^\\\\infty \\\\Gamma(1+iax)\\\\Gamma(1-iax) dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei = \\\\sqrt{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Gamma(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gamma function, the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46025\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46025\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59571,"title":"Compute a sum involving the zeta function","description":"Write a function to compute the sum\r\n\r\nfor , where  is the zeta function, the subject of Cody Problems 45939, 45988, and 45997.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.883px 8px; transform-origin: 111.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the sum\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"137.5\" height=\"45\" alt=\"S(x) = sum(zeta(n+1) x^n) for n = 1 to n = inf\" style=\"width: 137.5px; height: 45px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 8px; transform-origin: 10.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18.5\" alt=\"|x| \u003c 1\" style=\"width: 46.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEQAAAAlCAYAAAD7u09NAAAEdklEQVRoQ+2ZS6hPURTG3TkRIwYUBpRXeZZMDCgpSXlEuiOPgQxEMTAwoOgOZOCRgYwwkZQiMRB5TJBigDJh5FHM+X63s7Tvtl/nnHsu6pz6uqf/3mudvb/13PsOjOufEQwM9HyMZKAnxPOInpB/gJClWsNM4WrH4TpL+pfU/c5YewhknBHWCV86JgT1J4UZwpbSb9UhZI+UbhTWlir35kHGZWHlGJFhnzdPLCKlhJDJ0vxQeCkcEd5VX4Kg/cIcYa9wLkEUOj4Im4Q7DQltI/ZYwpcyaxzWX0IIDG8WZldkmKUhgueHsFp4llgxC4KQIiu12XlEljXfExZVe4h+ooSQ25JeI+AFPKeE8dX7G/3FS1JWRxYdRmgH+y1SiWHJJytSs0sIgd0bwtRKER7xSLguXBNyyfFve4ft3wyzTD9EvbmEEBQaKcf0nsoVPvnIPRW2Cl2X2RI3+ahJD4Ro6JYQYmQMZkIjtKDz+nGXMKXAk0o21HYORqHkT4gpyhFCdXgl0DucaLCa15XM3AayXYgcltLjQjRscoSQDL+lXCyz6p8afyKkEhmk01EuFqgCJL6JgvUrxP5pgapG/nIrhTV6y/X7J2FexhMtj0TbhBQh9BlHhVWC9R51rGb5g6p0KCFohBzQHBbMc0HYLdgabuqd0PPH0H1LoC1wx2KfM0Kia4oRYo0U7tUkVFhQ9uPeqtn82eo3umHOO5T09QIGwdt4aA6/VmM79ZeKYWM58pFnLtUxmFhjhHAG2CHkXDBmiSaEWAImLA56ZBi56MXdXaLcMYjMdcLJMI4R8l2K23hHE0JIwOQJcs50wQ1VS4bkCZ5BZ+MYDwJLcoh5SDSvhQjBla4IyQYm5RrVWJ2QIUQ/V3LmIW6/Y90yUyy/2BJo/EiqeEbu4Gnf8XX83k6IEGr1AqHtqZT7iLdCSVy7+YONbRPcDhiP5bgQ8gI3t+TyXdZIIUJgnLI3Gr1DSdnFOnaA5N33TDdHkFDdTbtjJR5t86Odc4gQNoElphWERW4K5JIPcrrMA4ht//LIcgShRI/ieo6Nccgs8WibHz1oxghhoyUZO0eIJcNU657yAPRbsg3lCMsfVkYJvfdCrNKQi+anDBQihAOQnWxR/EKg7t8VUnceIXIsj6QukKzcIu9bzuQZC+mw/MEYRHD4TF1PMj+Z00KEmFvFrB9KeilPwYo8sfbdLbf+HDfZ+mRZJ4xuQo1nuxDrqk1X8l4m15iZp/gbzp1P3PmpCyLXA/yEiQ4rt6EcgexzgepDyLjXmyEDYRi8nSNB9Mkd7hDEEjyEi3tZVOdIT1gsFJK3VamFthyjt7oo+En5D7UlhPhCTdp6u6jm1FrngqklD8PitS64mxBCzzBJyHWF/mbsbmVD5W2jsdkSHcU37ijLEWIVwFpdyiixmrtljy0UUjiu7xsjUjDe/TpemSPEypq7wVDyK7GUzbH7j9yptI7O0FySLt+q1SrkCKFU2b8d2MCQ0PVG2hLRSj5HSCvl/6NwT4hntZ6QnpB0IP8C3IMRNWT+n34AAAAASUVORK5CYII=\" width=\"34\" height=\"18.5\" alt=\"zeta(m)\" style=\"width: 34px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.517px 8px; transform-origin: 157.517px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the zeta function, the subject of Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45939\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45939\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45988\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45988\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45997\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45997\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function S = zetasum(x)\r\n  n = 1:Inf;\r\n  S = sum(zeta(n+1).*x.^n);\r\nend","test_suite":"%%\r\nx = 1/2;\r\nS = zetasum(x);\r\nS_correct = 1.386294361119891;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 2/3;\r\nS = zetasum(x);\r\nS_correct = 2.554818115119273;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 3/4;\r\nS = zetasum(x);\r\nS_correct = 3.650237868474732;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 5/6;\r\nS = zetasum(x);\r\nS_correct = 5.754911840473381;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 7/8;\r\nS = zetasum(x);\r\nS_correct = 7.811276998394322;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 8/9;\r\nS = zetasum(x);\r\nS_correct = 8.83072761223029;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 9/10;\r\nS = zetasum(x);\r\nS_correct = 9.84653927550954;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 10/11;\r\nS = zetasum(x);\r\nS_correct = 10.85964675709217;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 11/12;\r\nS = zetasum(x);\r\nS_correct = 11.87068966352595;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%% \r\nx = 0.232931374143;\r\nSS = zetasum(zetasum(x));\r\nSS_correct = 1.227707484938568;\r\nassert(abs(SS-SS_correct)/SS_correct\u003c1e-12)\r\n\r\n%%\r\nx = 1./primes(20);\r\ny = sum(arrayfun(@zetasum,x));\r\ny_correct = 3.2640541637441439;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('zetasum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'switch'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-20T17:57:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-20T13:37:10.000Z","updated_at":"2026-03-04T13:56:18.000Z","published_at":"2024-01-20T13:40:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the sum\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S(x) = sum(zeta(n+1) x^n) for n = 1 to n = inf\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(x) = \\\\sum_{n=1}^\\\\infty \\\\zeta(n+1) x^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"|x| \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e|x| \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"zeta(m)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\zeta(m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the zeta function, the subject of Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45939\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45939\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45988\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45988\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45997\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45997\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45964,"title":"Compute the nth Pythagorean prime","description":"Pythagorean primes have the form p = 4n+1, where n is an integer, and they can be written as the sum of squares of two integers. More information is available at \u003chttps://en.wikipedia.org/wiki/Pythagorean_prime Wikipedia\u003e, \u003chttps://www.youtube.com/watch?v=yu_aqA7mw7E Numberphile\u003e, and the \u003chttps://oeis.org/A002144 Online Encyclopedia of Integer Sequences\u003e. \r\n\r\nCompute the nth Pythagorean prime p and two integers a and b such that p = a^2+b^2","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.3px 7.8px; transform-origin: 109.3px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePythagorean primes have the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 4n+1\" style=\"width: 70px; height: 18px;\" width=\"70\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.9px 7.8px; transform-origin: 24.9px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209.25px 7.8px; transform-origin: 209.25px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is an integer, and they can be written as the sum of squares of two integers. More information is available at\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pythagorean_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=yu_aqA7mw7E\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eNumberphile\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.2333px 7.8px; transform-origin: 27.2333px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A002144\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOnline Encyclopedia of Integer Sequences\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.0167px 7.8px; transform-origin: 42.0167px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.85px 7.8px; transform-origin: 68.85px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth Pythagorean prime \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.2333px 7.8px; transform-origin: 55.2333px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and two integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.2833px 7.8px; transform-origin: 32.2833px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJEAAAAmCAYAAADEF3nuAAADdElEQVR4nO2bYZWrMBCFrwccYKAGUIACHOAAB7WwGiphPdRCNdRC348wL7c02ZSQBNLOdw7n7LaQMJPLZCahgKIoiqIoiqLEcQLQAWj3vpECfJOtRRgA3AE86DjjMx38TbYWowdwg3ky5X9x8s9eN5WJb7K1KFdYpwo9jGPvAJrid5SPb7K1KJPncwn1NTi2g5mmhsB5n2BrVTxgQv9RaQFc8Jzf+EQS4ui2VskJNuE8OhOsiLqI62uytSom1JMjnGFFFENNtlZDA+PUPmGbvzCDPCZsU7jNbV8irs1hqwIzGKkHO5eIWtgoFNN2Dlu/ngl51ktyiWiEFdGydA+RzNYGtjxkA/u5kwlxydqRaPG6vH/Cq9MHuKeEFtvzhVwiusBdWXX4e0sjia0tjEBkPpUVy27+7Or4bo0juwTH2idryUC2TDBOO8OWxKPj3CUNjAC2kktEy9XmCe4tDR675LZ21NllbpzVy0JaE5EeCY6YRBGwznAN2pXaF5GKD67zdXzcHW3EkENEPHY9jJCu8989nm0dF9cktZXn1Cteow2vQaxZyFreYMwRs3DWwDrP5RAZzBudfwncR4rSN4eIuLQ/4/Wh46Rb7Mhiq8ypvsSMRXT0xSgWkC9hDH0fi+RdvkP6PQfOWzOI0uZ9/tsFB4hssFJdsIhC+zJ7w0+mazAaPIf/lLCfthzv5oEcZR5wJ9Bsb2xqEITnVF+Y/cV6A/eAneqLmAP+FtkWBvw9TUiyewuc9+47PWyLz94e4fHdDD+5ISWvDYelq7OfgC2ALRKyhnYPqXMiTkN89rJPsiFzqm8q46R7bfgvXZ3Jk+4TCD+5sTvdW0gtIrHX5yOOzNns5Sjj6qTBtj2ZktWZ7EL7QrvsD+XKh94hpYjYXl+eKv2lWOPywvOla/1HQuENx9/d5dxuKSKp2Dj8NzADUfJ10JQi4iTeNZXJ99nHjufLZUcS+msQEPAcVXmto4UR0Ahrr7weekfZQiGliHgRcTk+koK41vySwyvRouYGNtneI2/YAj8UUgFxuOcqs7SAuP/UIpKxOyXuI8hyJfMMu6M7oI7o42KEzadGPNvRwdq6x09jUg+wbHOIvcXHjquu2nfoa2HAZ7wR8R9OMhUlCil3s5Z/yufC5XBtybNyAPg9GxWRshp5k9F16A/5FUVRFEX5VP4BLmDgO7xkXj0AAAAASUVORK5CYII=\" alt=\"p = a^2+b^2\" style=\"width: 72.5px; height: 19px;\" width=\"72.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [pp,a,b] = PythagoreanPrime(n)\r\n  pp = a^2+b^2;\r\nend","test_suite":"%%\r\nn = 1;\r\npp_correct = 5;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 5;\r\npp_correct = 37;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 25;\r\npp_correct = 257;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 125;\r\npp_correct = 1657;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 625;\r\npp_correct = 10313;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 3125;\r\npp_correct = 62497;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 15625;\r\npp_correct = 367229;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-19T01:58:26.000Z","updated_at":"2026-01-19T15:38:08.000Z","published_at":"2020-06-19T02:08:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePythagorean primes have the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 4n+1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 4n+1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer, and they can be written as the sum of squares of two integers. More information is available at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pythagorean_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=yu_aqA7mw7E\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNumberphile\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A002144\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOnline Encyclopedia of Integer Sequences\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth Pythagorean prime \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and two integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = a^2+b^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = a^2+b^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46582,"title":"Find jumping medalists","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 288px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 144px; transform-origin: 407.5px 144px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.308px 7.875px; transform-origin: 377.308px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eKey questions in number theory involve the distribution of prime numbers. For example, the Twin Prime Conjecture states that infinitely many twin primes, or two primes separated by 2, exist. This conjecture has not been proved, and progress is addressed in an interesting \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=vkMXdShDdtY\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003evideo from Numberphile\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.875px; transform-origin: 3.88333px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.983px 7.875px; transform-origin: 374.983px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem deals with the most common gap between primes up to a given number. John Conway dubbed this gap the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/JumpingChampion.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 56.8083px 7.875px; transform-origin: 56.8083px 7.875px; \"\u003ejumping champion\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 324.392px 7.875px; transform-origin: 324.392px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For numbers up to 20, the jumping champion is 2 because it occurs four times (between 3 and 5, 5 and 7, 11 and 13, and 17 and 19.) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 293.708px 7.875px; transform-origin: 293.708px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo me, the jumping champion is somewhat disappointing because 6 dominates until about 1.74\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 37.5px; height: 19px;\" width=\"37.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.45px 7.875px; transform-origin: 68.45px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, I will coin another term: the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.025px 7.875px; transform-origin: 56.025px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ejumping medalists\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 266.817px 7.875px; transform-origin: 266.817px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the three most common gaps between primes up to a given number. For numbers up to 20, the gold, silver, and bronze jumping medals (i.e., first, second, and third place) go to 2, 4, and 1, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 336.983px 7.875px; transform-origin: 336.983px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that determines the jumping medalists as well as the maximum gap. Award the medals as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46576-award-medals-to-winners\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46576\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.925px 7.875px; transform-origin: 206.925px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and return an empty vector for any medal that cannot be awarded.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.875px; transform-origin: 0px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [J1,J2,J3,Jmax] = jumpingMedalists(n)\r\n  % J1, J2, J3 = most, second-most, and third-most common gaps, respectively\r\n  % Jmax = maximum gap \r\n  \r\n  J = f(n);\r\nend","test_suite":"%%\r\nn = 2;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nassert(isempty(J1) \u0026\u0026 isempty(J2) \u0026\u0026 isempty(J3) \u0026\u0026 isempty(Jmax))\r\n\r\n%%\r\nn = 5;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = [1 2];\r\nJmax_correct = 2;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isempty(J2) \u0026\u0026 isempty(J3) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 7;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 2;\r\nJ2_correct = 1;\r\nJmax_correct = 2;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isempty(J3) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 11;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 2;\r\nJ2_correct = [1 4];\r\nJmax_correct = 4;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isempty(J3) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 20;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 2;\r\nJ2_correct = 4;\r\nJ3_correct = 1;\r\nJmax_correct = 4;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 100;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 2;\r\nJ2_correct = [4 6];\r\nJmax_correct = 8;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isempty(J3) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 3141;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 6;\r\nJ2_correct = 4;\r\nJ3_correct = 2;\r\nJmax_correct = 34;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 50011;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 6;\r\nJ2_correct = 2;\r\nJ3_correct = 4;\r\nJmax_correct = 72;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 6021023;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 6;\r\nJ2_correct = 12;\r\nJ3_correct = 2;\r\nJmax_correct = 154;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 12221997;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 6;\r\nJ2_correct = 12;\r\nJ3_correct = 2;\r\nJmax_correct = 154;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 2e8;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 6;\r\nJ2_correct = 12;\r\nJ3_correct = 4;\r\nJmax_correct = 248;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-10T02:33:57.000Z","updated_at":"2026-01-20T11:05:32.000Z","published_at":"2020-09-10T04:15:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eKey questions in number theory involve the distribution of prime numbers. For example, the Twin Prime Conjecture states that infinitely many twin primes, or two primes separated by 2, exist. This conjecture has not been proved, and progress is addressed in an interesting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=vkMXdShDdtY\\\"\u003e\u003cw:r\u003e\u003cw:t\u003evideo from Numberphile\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with the most common gap between primes up to a given number. John Conway dubbed this gap the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/JumpingChampion.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ejumping champion\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. For numbers up to 20, the jumping champion is 2 because it occurs four times (between 3 and 5, 5 and 7, 11 and 13, and 17 and 19.) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo me, the jumping champion is somewhat disappointing because 6 dominates until about 1.74\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\times 10^{35}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, I will coin another term: the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ejumping medalists\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, or the three most common gaps between primes up to a given number. For numbers up to 20, the gold, silver, and bronze jumping medals (i.e., first, second, and third place) go to 2, 4, and 1, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that determines the jumping medalists as well as the maximum gap. Award the medals as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46576-award-medals-to-winners\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46576\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and return an empty vector for any medal that cannot be awarded.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60401,"title":"Find primes and integers that solve an equation","description":"Write a function to find all primes  and non-negative integers  that solve the equation\r\n\r\nwhere  is an integer. If there are no solutions for a given value of , return p = [] and k = [].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.333px 8px; transform-origin: 103.333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find all primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.8083px 8px; transform-origin: 84.8083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and non-negative integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 8px; transform-origin: 72.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that solve the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"79.5\" height=\"19\" alt=\"p! + ap = k^2\" style=\"width: 79.5px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 179.692px 8px; transform-origin: 179.692px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is an integer. If there are no solutions for a given value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.1083px 8px; transform-origin: 24.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.95px 8px; transform-origin: 26.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ep = [] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.1px 8px; transform-origin: 23.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek = []\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,k] = Wilson(a)\r\n  p = primes(a); \r\n  k = randi(a);\r\nend","test_suite":"%%\r\na = 25;\r\n[p,k] = Wilson(a);\r\np_correct = 3;\r\nk_correct = 9;\r\nassert(isequal(p,p_correct) \u0026\u0026 isequal(k,k_correct))\r\n\r\n%%\r\na = -4;\r\n[p,k] = Wilson(a);\r\np_correct = 5;\r\nk_correct = 10;\r\nassert(isequal(p,p_correct) \u0026\u0026 isequal(k,k_correct))\r\n\r\n%%\r\na = 7;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str((k*p)^k)-'0');\r\ns_correct = 19;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\na = 10;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str((k*p)^k)-'0');\r\ns_correct = 18;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\na = 17;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str((k*p)^k)-'0');\r\ns_correct = 45;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\na = 21;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str((k*p)^p)-'0');\r\ns_correct = 45;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\na = 31;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str((k*p)^k)-'0');\r\ns_correct = 58;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\na = 12;\r\n[p,k] = Wilson(a);\r\nassert(isempty(p) \u0026\u0026 isempty(k))\r\n\r\n%%\r\na = -20;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str(k^p)-'0');\r\ns_correct = 25;\r\nassert(isequal(s,s_correct))\r\n\r\n%% \r\nA = -[1 2 24];\r\nj = randi(3);\r\n[~,k] = Wilson(A(j));\r\nassert(~k)\r\n\r\n%%\r\na = -19;\r\n[p,k] = Wilson(a);\r\nassert(isequal(p,k))\r\n\r\n%%\r\na = 22;\r\n[p,k] = Wilson(a);\r\nassert(isempty(p) \u0026\u0026 isempty(k))\r\n\r\n%%\r\nfiletext = fileread('Wilson.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-25T05:11:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-25T05:11:40.000Z","updated_at":"2026-02-02T04:13:20.000Z","published_at":"2024-05-25T05:11:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find all primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and non-negative integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that solve the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p! + ap = k^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep! + ap = k^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. If there are no solutions for a given value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek = []\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60331,"title":"Compute the area of a Q","description":"A figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \r\nWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 477.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 238.85px; transform-origin: 407px 238.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.408px 8px; transform-origin: 380.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 316.85px 8px; transform-origin: 316.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 166.85px; text-align: left; transform-origin: 384px 166.85px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Qarea(a,c)\r\n  y = a*c;\r\nend","test_suite":"%%\r\na = 1;\r\nc = sqrt(2);\r\ny = Qarea(a,c);\r\ny_correct = 2.121320343559643;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 2;\r\nc = sqrt(5);\r\ny = Qarea(a,c);\r\ny_correct = 5.031152949374527;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 5/2;\r\nc = sqrt(7);\r\ny = Qarea(a,c);\r\ny_correct = 7.011240974321167;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 3;\r\nc = sqrt(8);\r\ny = Qarea(a,c);\r\ny_correct = 8.013876853447540;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 3;\r\nc = sqrt(11);\r\ny = Qarea(a,c);\r\ny_correct = 11.055415967851332;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 4;\r\nc = sqrt(19);\r\ny = Qarea(a,c);\r\ny_correct = 19.070182877990447;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 5;\r\nc = sqrt(23);\r\ny = Qarea(a,c);\r\ny_correct = 23.019991311901052;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = sqrt(27);\r\nc = sqrt(29);\r\ny = Qarea(a,c);\r\ny_correct = 29.018512609609640;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 6;\r\nc = sqrt(31);\r\ny = Qarea(a,c);\r\ny_correct = 31.086684359134285;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = sqrt(43);\r\nc = sqrt(41);\r\ny = Qarea(a,c);\r\ny_correct = 41.011626258563474;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('Qarea.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-18T15:50:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-18T03:49:34.000Z","updated_at":"2026-03-04T13:41:21.000Z","published_at":"2024-05-18T03:49:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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an equation involving primes and fractions","description":"Write a function to find pairs of primes  and  satisfying the equation\r\n\r\nwhere  is an integer. The function should take a number  as input and produce the triples , , and  such that . If there are no solutions, the function should return three empty vectors.\r\nThis problem is adapted from one in the 2012 European Girls’ Math Olympiad. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 73px; transform-origin: 343px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find pairs of primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e satisfying the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136\" height=\"35\" alt=\"p/(p+1) + (q+1)/q = 2n/(n+2)\" style=\"width: 136px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer. The function should take a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and produce the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"18\" alt=\"p \u003c= x\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If there are no solutions, the function should return three empty vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis problem is adapted from one in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.egmo2012.org.uk/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e2012 European Girls’ Math Olympiad\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,q,n] = EGMO2012no5(x)\r\n  p = primes(x); q = primes(x); n = p./(p+1) + (q+1)./q; \r\nend","test_suite":"%%\r\nx = 1;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(isempty(p) \u0026\u0026 isempty(q) \u0026\u0026 isempty(n))\r\n\r\n%%\r\nx = 2;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(all(p==2) \u0026\u0026 isequal(q,[5 7]) \u0026\u0026 isequal(n,[28 19]))\r\n\r\n%%\r\nx = 20;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 200;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402 3778 7306 14758 21166 42226 47302 77002 90898 130678 148606 158002];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 2000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 63;\r\nsum_correct = 265170305;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\n\r\n%%\r\nx = 20000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 344;\r\nsum_correct = 150118037395;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2000000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 14873;\r\nsum_correct = 27402595128;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2e8;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 813373;\r\nsum_correct = 152663390088360;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('EGMO2012no5.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-30T13:15:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-30T05:04:32.000Z","updated_at":"2025-12-14T08:06:30.000Z","published_at":"2022-12-30T05:05:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find pairs of primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e satisfying the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p/(p+1) + (q+1)/q = 2n/(n+2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{p}{p+1} + \\\\frac{q+1}{q} = \\\\frac{2n}{n+2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. The function should take a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produce the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p \u0026lt;= x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep \\\\le x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there are no solutions, the function should return three empty vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is adapted from one in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.egmo2012.org.uk/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2012 European Girls’ Math Olympiad\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59521,"title":"Integrate a power tower","description":"Write a function to compute this integral\r\n\r\nwhere . That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52px; transform-origin: 407px 52px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.783px 8px; transform-origin: 122.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute this integral\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"135\" height=\"44\" alt=\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\" style=\"width: 135px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.3px 8px; transform-origin: 226.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = intPowerTower(a)\r\n  I = integral(x^x^x^x^x^x^x^x,0,a);\r\nend","test_suite":"%%\r\na = 0;\r\nI = intPowerTower(a);\r\nassert(abs(I)\u003c1e-6)\r\n\r\n%%\r\na = 1/100;\r\nI = intPowerTower(a);\r\nI_correct = 0.00975627404012066;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/20;\r\nI = intPowerTower(a);\r\nI_correct = 0.04621245261821598;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/10;\r\nI = intPowerTower(a);\r\nI_correct = 0.0886781687569094;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/5;\r\nI = intPowerTower(a);\r\nI_correct = 0.1685639964895788;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.2071658901263798;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/8;\r\nI = intPowerTower(a);\r\nI_correct = 0.30215124860335973;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/2;\r\nI = intPowerTower(a);\r\nI_correct = 0.3972053202401857;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 2/3;\r\nI = intPowerTower(a);\r\nI_correct = 0.5277402852630483;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.5959989560650945;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 5/6;\r\nI = intPowerTower(a);\r\nI_correct = 0.6671963910854818;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1;\r\nI = intPowerTower(a);\r\nI_correct = 0.822467033424113;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = (rand+3)/4;\r\nI = intPowerTower(a);\r\nI_correct = polyval([0.3875275 -0.9886411 1.132527 0.1505356 0.1405179],a);\r\nassert(abs(I-I_correct)\u003c5e-6)\r\n\r\n%%\r\nfiletext = fileread('intPowerTower.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'find') || contains(filetext,'switch'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-03T15:06:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-31T18:50:11.000Z","updated_at":"2026-01-28T06:58:04.000Z","published_at":"2023-12-31T18:50:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute this integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^a {(x^x)^{(x^x)^{(x^x)\\\\ldots}} dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \\\\le a \\\\le 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":56593,"title":"List the nth term of Rozhenko’s inventory sequence","description":"Consider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\r\n0\r\n1, 1, 0\r\n2, 2, 2, 0\r\n3, 2, 4, 1, 1, 0\r\n4, 4, 4, 1, 4, 0\r\nWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19th term is 4. \r\nThis sequence produces interesting plots and music. See the related Numberphile video for more. \r\nWrite a function to report the th term of this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 345px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 172.5px; transform-origin: 407px 172.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.6px 8px; transform-origin: 374.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1, 1, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.2167px 8px; transform-origin: 27.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2, 2, 2, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3, 2, 4, 1, 1, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4, 4, 4, 1, 4, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e term is 4. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.425px 8px; transform-origin: 112.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis sequence produces interesting \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A342585/graph\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eplots\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/play?seq=A342585\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003emusic\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 8px; transform-origin: 18.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. See \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=rBU9E-ZOZAI\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ethe related Numberphile video\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.8833px 8px; transform-origin: 31.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for more. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.1px 8px; transform-origin: 90.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to report the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5583px 8px; transform-origin: 78.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Rozhenko(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 19;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny_correct = 5;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 347;\r\ny_correct = 25;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 823;\r\ny_correct = 27;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 1997;\r\ny_correct = 20;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 4721;\r\ny_correct = 68;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 13859;\r\ny_correct = 18;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 19793;\r\ny_correct = 7;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 24677;\r\ny_correct = 51;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 41903;\r\ny_correct = 357;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 25537;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(Rozhenko(Rozhenko(n))),y_correct))\r\n\r\n%%\r\nn = [1 4 8 14 20 28 37 46 57 69 82 95 110 125 142 159 177 196 216 238 260 285 310 335 362 390 418 448 478 511];\r\na = arrayfun(@Rozhenko,n);\r\ns_correct = 0;\r\nassert(isequal(sum(a),s_correct))\r\n\r\n%%\r\nfiletext = fileread('Rozhenko.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-11-13T14:07:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-13T04:07:55.000Z","updated_at":"2026-01-24T12:19:36.000Z","published_at":"2022-11-13T04:08:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1, 1, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2, 2, 2, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3, 2, 4, 1, 1, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4, 4, 4, 1, 4, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e term is 4. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis sequence produces interesting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A342585/graph\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eplots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/play?seq=A342585\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emusic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. See \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=rBU9E-ZOZAI\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe related Numberphile video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to report the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term of this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50948,"title":"Identify prime words","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6083px 7.91667px; transform-origin: 13.6083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=9CcI5M1LfRs\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eNumberphile video on evil primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 236.375px 7.91667px; transform-origin: 236.375px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, Tony Padilla introduced the “Jesus prime” 105,192,119, which is formed by concatenating the positions of the letters of ‘Jesus’ in the English alphabet: 10, 5, 19, 21, 19. In general, a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.625px 7.91667px; transform-origin: 34.625px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eprime word\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6167px 7.91667px; transform-origin: 20.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e could be defined as a word such that the number formed by concatenating the positions of the letters in the alphabet is prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.425px 7.91667px; transform-origin: 368.425px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a string and identifies prime words. It should delete apostrophes and hyphens (e.g. “don’t” = “dont”, “un-ionized” = “unionized”) and treat other punctuation as spaces. The function should return an array of 0’s and 1’s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isPrimeWord(s)\r\n  tf = isprime(s);\r\nend","test_suite":"%%\r\nassert(isPrimeWord('Croatia'))\r\n\r\n%%\r\nassert(~isPrimeWord('Serbia'))\r\n\r\n%%\r\nassert(isPrimeWord('frenetic'))\r\n\r\n%%\r\nassert(~isPrimeWord('frantic'))\r\n\r\n%%\r\nassert(isPrimeWord('smiling'))\r\n\r\n%%\r\nassert(~isPrimeWord('frowning'))\r\n\r\n%%\r\nassert(isPrimeWord('ziti'))\r\n\r\n%%\r\nassert(~isPrimeWord('spaghetti'))\r\n\r\n%%\r\nassert(isPrimeWord('tick'))\r\n\r\n%%\r\nassert(~isPrimeWord('tock'))\r\n\r\n%%\r\nassert(isPrimeWord('madam'))\r\n\r\n%%\r\nassert(~isPrimeWord('Adam'))  \r\n\r\n%%\r\nassert(isPrimeWord('RFQ'))\r\n\r\n%%\r\nassert(~isPrimeWord('FAQ'))\r\n\r\n%%\r\nassert(isPrimeWord('Jesus'))\r\n\r\n%%\r\nassert(~isPrimeWord('Moses'))  \r\n\r\n%%\r\nassert(isPrimeWord('adieu'))\r\n\r\n%%\r\nassert(~isPrimeWord('milieu'))\r\n\r\n%%\r\nassert(isPrimeWord('wallow'))\r\n\r\n%%\r\nassert(~isPrimeWord('swallow'))  \r\n\r\n%%\r\ns = 'slim pickings';\r\nassert(all(isPrimeWord(s)))\r\n\r\n%%\r\ns = 'mellow fellow';\r\nassert(all(isPrimeWord(s)))\r\n\r\n%%\r\ns = 'Ms. Zadora stuck a cornucopia full of Bing cherries into her knapsack.';\r\ntf_correct = [1 1 1 0 1 0 0 1 0 0 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%%\r\ns = 'The dog and pig are going to India.';\r\ntf_correct = [0 1 0 1 0 1 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%%\r\ns = 'Liam, is Mauritius in Africa? I know that Mali and Libya are.';\r\ntf_correct = [1 1 1 0 1 0 0 0 1 0 1 0];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n\r\n%% Maria Bamford\r\nq = char(39);\r\ns = ['I was in a lot of plays. We had a weird drama teacher in that he was incredibly enthusiastic about a high school drama program and would talk to all the kids for hours. He ended up marrying one of the kids, but that' q 's neither here nor there.'];\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[28 32 42]))\r\n\r\n%% Maria Bamford\r\nq = char(39);\r\ns = ['I do wanna get married. It just sounds great. You get to go grocery shopping together, rent videos, and the kissing and the hugging and the kissing and the hugging under the cozy covers. Mmmm! But sometimes I worry that I don' q 't wanna get married as much as I want to get dipped in a vat of warm, rising bread dough. That might feel pretty good, too.'];\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[3 15 34 43]))\r\n\r\n%% Monty Python\r\ns = 'I cut down trees, I eat my lunch, I go to the lavatory. On Wednesday I go shopping and have buttered scones for tea.';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[4 18]))\r\n\r\n%% Monty Python\r\ns = 'Strange women lying in ponds, distributing swords, is no basis for a system of government!';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[8 10]))\r\n\r\n%% Monty Python\r\ns = 'My hovercraft is full of eels.';\r\ntf_correct = [0 0 1 0 0 1];\r\nassert(isequal(isPrimeWord(s),tf_correct))\r\n    \r\n%% Basil Fawlty\r\ns = 'Well may I ask what you expected to see out of a Torquay hotel bedroom window? Sydney Opera House perhaps? The Hanging Gardens of Babylon? Herds of wildebeest sweeping majestically';\r\ntf = isPrimeWord(s);\r\nassert(isequal(find(tf),[18 23]))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-03-14T22:44:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-14T16:24:34.000Z","updated_at":"2026-01-20T19:15:07.000Z","published_at":"2021-03-14T16:29:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=9CcI5M1LfRs\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNumberphile video on evil primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, Tony Padilla introduced the “Jesus prime” 105,192,119, which is formed by concatenating the positions of the letters of ‘Jesus’ in the English alphabet: 10, 5, 19, 21, 19. In general, a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprime word\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e could be defined as a word such that the number formed by concatenating the positions of the letters in the alphabet is prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a string and identifies prime words. It should delete apostrophes and hyphens (e.g. “don’t” = “dont”, “un-ionized” = “unionized”) and treat other punctuation as spaces. The function should return an array of 0’s and 1’s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57447,"title":"Compute a nested cube root","description":"Consider the quantity . Write a function to compute  without using loops or recursion. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.075px 8px; transform-origin: 68.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the quantity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" alt=\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\" style=\"width: 249px; height: 19.5px;\" width=\"249\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.875px 8px; transform-origin: 90.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Write a function to compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.575px 8px; transform-origin: 71.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e without using loops or recursion. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = nestedCubeRoot(a)\r\n  y = nthroot(a+nthroot(a+nthroot(a+nthroot(a,3),3),3),3);\r\nend","test_suite":"%%\r\na = 6;\r\nassert(abs(nestedCubeRoot(a)-2)\u003c1e-14)\r\n\r\n%%\r\na = 24;\r\nassert(abs(nestedCubeRoot(a)-3)\u003c1e-14)\r\n\r\n%%\r\na = 120;\r\nassert(abs(nestedCubeRoot(a)-5)\u003c1e-14)\r\n\r\n%%\r\na = 336;\r\nassert(abs(nestedCubeRoot(a)-7)\u003c1e-14)\r\n\r\n%%\r\na = 1320;\r\nassert(abs(nestedCubeRoot(a)-11)\u003c1e-14)\r\n\r\n%%\r\na = 15/8;\r\nassert(abs(nestedCubeRoot(a)-3/2)\u003c1e-14)\r\n\r\n%%\r\na = 2040/2197;\r\nassert(abs(nestedCubeRoot(a)-17/13)\u003c1e-14)\r\n\r\n%%\r\na = 9048/12167;\r\nassert(abs(nestedCubeRoot(a)-29/23)\u003c1e-14)\r\n\r\n%%\r\na = 29520/29791;\r\nassert(abs(nestedCubeRoot(a)-41/31)\u003c1e-14)\r\n\r\n%%\r\na = 117384/226981;\r\nassert(abs(nestedCubeRoot(a)-73/61)\u003c1e-14)\r\n\r\n%%\r\na = 2259912/3869893;\r\nassert(abs(nestedCubeRoot(a)-191/157)\u003c1e-14)\r\n\r\n%%\r\nfiletext = fileread('nestedCubeRoot.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'switch') || contains(filetext,'for') || contains(filetext,'while') || length(strfind(filetext,'nestedCubeRoot')) \u003e 1;\r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-21T13:18:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-21T13:13:13.000Z","updated_at":"2026-03-04T12:08:30.000Z","published_at":"2022-12-21T13:18:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = (a+(a+(a+(a+\\\\ldots)^{1/3})^{1/3})^{1/3})^{1/3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Write a function to compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e without using loops or recursion. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58946,"title":"Count block fountains","description":"A block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \r\nWrite a function to compute the number of block fountains with  circles on the first row. For example, there are five block fountains with three circles on the first row. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 429.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 214.85px; transform-origin: 407px 214.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 364.85px 8px; transform-origin: 364.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.125px 8px; transform-origin: 195.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the number of block fountains with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.958px 8px; transform-origin: 176.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e circles on the first row. For example, there are five block fountains with three circles on the first row. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 327.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 163.85px; text-align: left; transform-origin: 384px 163.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"543\" height=\"322\" style=\"vertical-align: baseline;width: 543px;height: 322px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = blockFountain(n)\r\n  y = factorial(n);\r\nend","test_suite":"%%\r\nassert(isequal(blockFountain(3),5))\r\n\r\n%%\r\nassert(isequal(blockFountain(5),34))\r\n\r\n%%\r\nassert(isequal(blockFountain(8),610))\r\n\r\n%%\r\nassert(isequal(blockFountain(14),196418))\r\n\r\n%%\r\nassert(isequal(blockFountain(14),196418))\r\n\r\n%%\r\nassert(isequal(blockFountain(23),1134903170))\r\n\r\n%%\r\nassert(isequal(blockFountain(28),139583862445))\r\n\r\n%%\r\nassert(isequal(blockFountain(33),17167680177565))\r\n\r\n%%\r\nassert(isequal(blockFountain(35),117669030460994))\r\n\r\n%%\r\nfiletext = fileread('blockFountain.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-03T17:54:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2023-09-03T17:54:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-02T14:47:44.000Z","updated_at":"2026-01-26T19:21:38.000Z","published_at":"2023-09-02T14:47:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the number of block fountains with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e circles on the first row. For example, there are five block fountains with three circles on the first row. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"322\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"543\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46003,"title":"Compute Khinchin's constant","description":"Khinchin's constant K_0 = 2.684542001... (also written \"Khintchine's constant\") has the amazing property that it is the limiting value of the geometric mean of the partial quotients from a continued fraction expansion of almost all numbers. In other words, if a number x is expanded as \r\n\r\n\u003c\u003chttps://wikimedia.org/api/rest_v1/media/math/render/svg/d60c339a507116862b2c43d6d447db411c4277d3\u003e\u003e\r\n\r\nthen \r\n\r\n\u003c\u003chttps://wikimedia.org/api/rest_v1/media/math/render/svg/8a05ee602e42ba03dcfa068f518a0664eebc3bc0\u003e\u003e\r\n\r\nMore information is available at \u003chttps://en.wikipedia.org/wiki/Khinchin%27s_constant Wikipedia\u003e, \u003chttps://mathworld.wolfram.com/KhinchinsConstant.html Wolfram MathWorld\u003e, the \u003chttps://oeis.org/A002210 Online Encyclopedia of Integer Sequences\u003e, and \u003chttps://www.youtube.com/watch?v=VDD6FDhKCYA Numberphile\u003e. \r\n\r\nCompute Khinchin's constant. The test suite will check for a difference of 10^{-12}. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 298.833px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 149.417px; transform-origin: 407px 149.417px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.6333px; text-align: left; transform-origin: 384px 31.6333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.0167px 7.91667px; transform-origin: 62.0167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eKhinchin's constant \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"K_0\" style=\"width: 18px; height: 20px;\" width=\"18\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 312.983px 7.91667px; transform-origin: 312.983px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 2.684542001... (also written \"Khintchine's constant\") has the amazing property that it is the limiting value of the geometric mean of the partial quotients from a continued fraction expansion of almost all numbers. In other words, if a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.0167px 7.91667px; transform-origin: 49.0167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is expanded as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.6667px; text-align: left; transform-origin: 384px 42.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.91667px; transform-origin: 13.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-69px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Continued fraction expansion of x\" style=\"width: 160.5px; height: 85.5px;\" width=\"160.5\" height=\"85.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.9px 7.91667px; transform-origin: 24.9px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n approaches infinity\" style=\"width: 46.5px; height: 18px;\" width=\"46.5\" height=\"18\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.6333px; text-align: left; transform-origin: 384px 10.6333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6px 7.91667px; transform-origin: 13.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQsAAAAqCAYAAACk0n51AAAGpUlEQVR4nO2d65HiMBCEOwcyIAEScAQbARmQARmQAjEQwuZACsRACns/5C43Or1s+c18Va6rBWPJstSaGY18gGEYhmEYhmEYhmEYxiScAVyXroRhGPNyAHBp/y3lF8BxmuoYhrFGzgDeAP5QLhZHOLEwDONLuAH4gROKPmJxhRMZYyFO6GcGGoZywHC3oK9YvAaWY4zAGcB96UoYm+YA4IFhM34fsThihr7awJk9L3SV43GHC7CQK5xPpOe82s/3NvuaUBhj8kR/wegjFle4sRyiactu5O/U+VnUR/rDp0jEzrtjn5HXHzgR3JsAGstxgOtTpx6/6SMWIRfkCCcKvM4Jbsw+2r+fPerygYpAbKCc0EVoY2KydY5w9zhYdQ0jQt9JqFQsGsSt4AM6Ybi3deC1B8c47vi0GHwoFC/seyDdYctPxnT8wrn9JZSKxR3xMUkj4CnlNu1npfX4D41Z+L7Vuf187wkfR7j73LMYGsvCsVQyjkrFImUh0AjQc+ia/AR/kYGDhAdvhJHcP+wziOlzhy0/GdPzRllKdolY5NK7aQSoAcBFikHj+SIVe7YXObUFvfE9iR5v2AqIMT0PlE1KJWKRsvZpBPhl0UsYBK0H+jEUjyf6RW+3DP24IcJ4hmv8Z/vvvf3sCSdAY1hkDdxzYhkPODOSs8QYrtMcZaydOdqAbkDOFcmJRS69my6PxiYYw7hiYMYnVzioQhSKueMTHLC1x5CVGj7APp3hhE4Q1P9TS602WKquoG4qOkkZtYI0RxlrZ842YD9PxQx0LMQm7NxgZ7xC+zT7+QMDApzaGP4xKABSwZJiwYYt7QxcHQots+p91CwxH+DEKHYdlvFYeRlrZ+42YP+IxRp+0M38PEKTWG4iuuD/+zm01xs0tjVpg8s6Gr/4FmhmlqD5JqFGL5kVcmgHjs0AtYI0RxlrZ4k2YO7D4KVLzJTe7aPp21zxULekj09zhGvQqlTShSgVC2bipWYaCjCDxTHOiIsJTeJYEo8KUshdZEpv6lnUlnGSMua2Qseitg2GUuuizr7DlArHg51KrY134bWu6EzyI9xA2ZLpWioWfvpsCM5UMeVv5JycZRKbzWgB+oLEmfIlZVDY9LyaMgB3b2+4duPksqXnDdS3QQ21YjH7Er+mePvBG03Syq0J8zra4Fy2qTG15qRELNTqig0M7YAh5b+gS/uNiQXrEpvttB6+IP3i8zmoy3T1zhtaxhmf4qPW1pZWz2raoJaaa6bSuydD4xN+5z/Ld7nAHzuKb6ZxpaDUfFsywElzNIW2ScwEVLcudd88zxcLTZCLdQi1brQetOh8dCm8tgxEflOVFbgAtW1QQy7AuUrUeggNMO34sQblakrIXeEKQ+ngXcPSaWpm1P0zISFQSy0XHI6JRU6QuNEtJOLHSP3ZrqxTTRkxbih3WdfAFG1QSk1OzyL4Kd6pTpY6h40eGhwcgFvIiuRAT82MKp5+52HOBQWY9/yDcLvFxEJnM/87xiP4W822LVmzp0s4dhl0Q/oGtU8oszrHPg8Ypw34Nwc9t4TnRICW3mZcNlXW1LZZHSChgIxG/vt8tzYY7E2ZhmpZ6INmarxaFmd0WZyhti2xLNRCYge+4DOAyrJTHc+3msYso2m/e6HfTJkarFOeR2rb4IpuYrigy+Jl7k1KtBgc3gwqAqnIqj6EkOm0F7EAujTfGGppcTMQH3zjff9EOgs2Jhb+0vUNnYnPTq3PrWRGf+Ez0DxWGUweUne21LoocXGnOI+M0QaayMX2ZT1SYrGZPUhUQN/P998TeEbXeKlz9yQWJduHL+gGB18pqLt0ufku9xaxmFgAn0urvJbO6gzGPpAfnKzvlGUAndVVOgg4U+f2H419nlLTBrREX/i0uHP9nRPKZlyQMdGXa/hoHvpW8GfhqUiJxVgwjjLXng4O1m9A3RhOCiUvlfnqlyvFtsEC/VdD1kCDfsu9Q5laLOh7z5lJ+4vvGQghSyq3fMyVwz2/QCpLKs9iiybXDdNbQ1OKxaG9fkgoplyue2JjuQMVhPp8LrGPgdOvJpXBuYlAToAHpn2wU4mFRvN9uG+nFn2tPJnLIlsD7NvqcjGGQZH2+/0t8NnXwmBog8916q2+A+GA7iU2U1x7qrek64uMQscYg1kD3cwz+MX2LMihMF6hwst4RcgVs/+DJgCTUq7YT8cZ+92julNTd2yOUUbo2nqMJXz6nC/Yz7MuhUvG/jMLvT/iGPjMMAzDMAzDMAzDMAzDMAzDMAzDMAzDWC//AEaigcAXd+7JAAAAAElFTkSuQmCC\" alt=\"K_0 is the nth root of the product of a_1 through a_n\" style=\"width: 133.5px; height: 21px;\" width=\"133.5\" height=\"21\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.8667px 7.91667px; transform-origin: 96.8667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMore information is available at\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Khinchin%27s_constant\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/KhinchinsConstant.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWolfram MathWorld\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6167px 7.91667px; transform-origin: 13.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A002210\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOnline Encyclopedia of Integer Sequences\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5667px 7.91667px; transform-origin: 15.5667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=VDD6FDhKCYA\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 39.7px 7.91667px; transform-origin: 39.7px 7.91667px; \"\u003eNumberphile\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.417px 7.91667px; transform-origin: 226.417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute Khinchin's constant. The test suite will check for a difference of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"10^{-12}\" style=\"width: 35px; height: 19.5px;\" width=\"35\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function K0 = KhinchinsConstant\r\n  K0 = ...;\r\nend","test_suite":"%%\r\nassert(abs(KhinchinsConstant-2.68545200106530644)\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('KhinchinsConstant.m');\r\nx = ~isempty(strfind(filetext, 'A002210')) || ~isempty(strfind(filetext, '2.68545200106')) ||...\r\n    ~isempty(strfind(filetext, 'char')) || ~isempty(strfind(filetext,'str2num')) ||...\r\n    ~isempty(strfind(filetext, 'urlread'));\r\nassert(~x, 'Illegal approach. Try one of the formulas on the Wolfram MathWorld page.')","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-30T04:17:42.000Z","updated_at":"2026-01-24T11:49:57.000Z","published_at":"2020-06-30T05:17:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eKhinchin's constant \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K_0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 2.684542001... (also written \\\"Khintchine's constant\\\") has the amazing property that it is the limiting value of the geometric mean of the partial quotients from a continued fraction expansion of almost all numbers. In other words, if a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is expanded as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Continued fraction expansion of x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = a_0+\\\\frac{1}{a_1+\\\\frac{1}{a_2+\\\\frac{1}{a_3 + \\\\frac{1}{\\\\ddots}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n approaches infinity\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\\\\to\\\\infty\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K_0 is the nth root of the product of a_1 through a_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_0 = (a_1a_2a_3\\\\ldots a_n)^{1/n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore information is available at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Khinchin%27s_constant\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/KhinchinsConstant.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWolfram MathWorld\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A002210\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOnline Encyclopedia of Integer Sequences\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=VDD6FDhKCYA\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNumberphile\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute Khinchin's constant. The test suite will check for a difference of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"10^{-12}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10^{-12}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51975,"title":"Compute a sum of Ramanujan","description":"Srinivasa Ramanujan defined the following function:\r\n\r\nWrite a function to compute  for various values of . See also Cody Problems 45960 and 46000.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 160.675px 7.79167px; transform-origin: 160.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSrinivasa Ramanujan defined the following function:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"phi(a) = 1+2 Sum[1/((a k)^3 - a k),{k,1,infinity}]\" style=\"width: 162.5px; height: 45px;\" width=\"162.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.9917px 7.79167px; transform-origin: 86.9917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"phi(a)\" style=\"width: 32.5px; height: 18.5px;\" width=\"32.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.5083px 7.79167px; transform-origin: 66.5083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for various values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.85px 7.79167px; transform-origin: 82.85px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. See also Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45960\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e45960\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e46000\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Ramanujanphi(a)\r\n  y = f(a);\r\nend","test_suite":"%%\r\na = 2;\r\ny_correct = 2*log(2);\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 3;\r\ny_correct = log(3);\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 4;\r\ny_correct = (3/2)*log(2);\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 5;\r\nphi = (1+sqrt(5))/2;\r\ny_correct = (sqrt(5)/5)*log(phi)+(1/2)*log(5);\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 6;\r\ny_correct = (1/2)*log(3)+(2/3)*log(2);\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 7;\r\ny_correct = (2/7)*(log(14)+2*cos(pi/7)*log(cos(pi/14))+2*log(cos(3*pi/14))*sin(pi/14)-2*log(sin(pi/7))*sin(3*pi/14));\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 8;\r\ny_correct = log(2)+(sqrt(2)/8)*log((2+sqrt(2))/(2-sqrt(2)));\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 12;\r\ny_correct = (1/2)*log(2)+(1/4)*log(3)+(sqrt(3)/6)*log((sqrt(3)+1)/(sqrt(3)-1));\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = 18;\r\nb = pi/9;\r\ny_correct = (1/9)*(log(2)+2*log(6)+log(sqrt(3)/2)+2*cos(b)*log(cos(b/2))+2*cos(2*b)*log(cos(b))-2*cos(b)*log(sin(b/2))-2*cos(2*b)*log(sin(b))+2*log(cos(2*b))*sin(b/2)-2*log(sin(2*b))*sin(b/2));\r\nassert(abs(Ramanujanphi(a)-y_correct)\u003c1e-14)\r\n\r\n%%\r\na = [11 13 17];\r\nsum_correct = 3.003409919427940;\r\nassert(abs(sum(Ramanujanphi(a))-sum_correct)\u003c1e-14)\r\n\r\n%%\r\na = [36 54 72 100];\r\ny_correct = [1.0000515628258977 1.0000152722224909 1.0000064421348023 1.000002404321212];\r\nk = randi(4);\r\nassert(abs(Ramanujanphi(a(k))-y_correct(k))\u003c1e-14)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2021-06-05T14:29:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-05T14:22:18.000Z","updated_at":"2026-01-20T21:12:40.000Z","published_at":"2021-06-05T14:23:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSrinivasa Ramanujan defined the following function:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phi(a) = 1+2 Sum[1/((a k)^3 - a k),{k,1,infinity}]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\phi(a) = 1+2\\\\sum_{k=1}^\\\\infty\\\\frac{1}{(a k)^3 – a k}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phi(a)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\phi(a)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for various values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. See also Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45960\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45960\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e46000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60456,"title":"Compute a sum","description":"Write a function to compute the following sum\r\n\r\nAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 126px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 63px; transform-origin: 407px 63px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.067px 8px; transform-origin: 141.067px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following sum\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPcAAABaCAYAAABkDsBjAAASJklEQVR4Xu2dV8g2RxXHv4AXImiwXNn4UHMRElCCDaOCQqwgir1cvKDEiiD2GAmCLRaCYidCCIoliiJELBAhEdFYUBQULEgQr6zkwhtBz0/3/+V88872md1nnz0Lh7fs7O7MmfOfOW1mLjgTV3AgOHCUHLjgKFsVjQoOBAfOBLhDCIIDR8qBAPeRdmw0KzgQ4A4ZCA4cKQcC3EfasdGs4ECAO2QgOHCkHAhwH2nHRrOCAwHukIHgwJFyIMA9rGMfbsWe2hT9iv38Q/LYfe3vi43+nLk37AtRKjhQmAMB7n6GftGKPNLo7+7n2+33TzePvsV+Xute8237/TUB8n7GRom6HAhwd/MX4F5p9Bijvxq9yOgLzSNPsJ8PbP7+kv38mdGTjZjhf2L0tOaZuj0Ybw8OtHAgwN0tGn9rZmFmb12aqX9v/7iPkZ/FKUPZFxo90+ibIXnBgbU4EOBu5zx29s9bQPqtZoZmxmY295eee6/98x1rdWx8NzgQ4G6XgcfbrduMXmUk+1qldU92eOpg+48VDHAHvlblQIC7nf0PsVuo3jn7+RP2/1c3j+JAw77Whef8L0bY5N9ftXfj47vmQIC7u/u9+n1jU/T19vPRRs8yusHooUZePccmf77Ro3YtWdH41TkQ4O7uAuzn7xnd2xVDFQfYzMrc/2oDcGZ57lFW3vXVOzgqsF8OBLj7+x41+wqjBxvdYfRdI8JiutL73rPe//YoERyoxIEAdyXGxmuDA2tzIMC9dg/E94MDlTgQ4K7E2HhtcGBtDgS41+6B+P6aHMAheqdRmqewZp2KfTvAXYyV8aINcIDko6uNcIKyGIjraNOE9wRu0kRPDkgA/2F1SVNXD6h6R12VHztw389+99GPQ244g9MlRkRu/mn0gUaGkOufGp2X7rwncL/SGv+ppOeIS99euDf9rND36shi6+NQnftKTiL7cEvJRoD7umZgQuO4vAE5KxdJpoLOmRh7Ajdi4kdsiU1NtUwjLbYds7RPhuH7uYUndcR5e28FgFyl18YrPZh3v9WI2W9L1++ssqxGJJ/i1uYncg2wMTV2C27yxRmt04yz85hSsaefYe8mfVW7uvCp80bbit/e2qtZfMP1CKNfFKw8fXBz876taU5a74DGCbgZ+DRYpWscdnniiO9cyczS6hkz+g0NsGP1WB65tcCtRT8A5CKjrdjbcEmmpa+75PmUFrI3tVxi5Fd16X9Lq2iMuB83esoGhazgRNr6qlrgRq1NF/ss0Z4S39BGIF5W32MvvsrolBayV3ADLGw6hUPE+DXUNOrBLL50Tjraw+saQWf2wnvPyjeZDeIFquD9jR5ndFlT/ib7KVtVW1EBmJLbS9UAt9Ra+lvr9PGFvNHJAuot4ClpCqTAxgdzz4anZ5tvpXsGeAewTDd2BuLyGofsbexw2rdbm9szuW3F19Kqmgaapby20hjYCgoBZzdXwK0dZOBRqvZdav97m5F8FdjBfzJiYNLAwPu4SmlANcCdAuZNVl80p88YATKt0acdtUJk8J9Vg+8y0uTyYvs9Hdzl/GW14cNc/3jbWoMVjllWL15odM5BuNeZu5HDczaM/ubnKceEv1npd4SO1Wa1M6W8xpLbYUaAynnxffgIIFPmeiNmHO1MA3ty753CthrgllqLhgFomAnfaSS72+9kW6odbW33pmE6kPiBVj4ZDUy+XipHW+iP3ca525isDvf3a3fsFGGf+4wHdpsTT4DqAj4z81kjZncJk98VtpT3vwa49U7tsPNaB2z46wep2o5Ozcw5Z67saOqkUK1U+XR3H/7PdcqMGDNz03DsLl0/sF/0IUaVH+Y+MFciF3geof+REULpr9IhmAWa0vkJDWIIdm4zCS/YKUD9vU/a86iDL3XAkDCOsbmlCczhCwMMtuaQy0dJ2va+8+0sZV7k6tYVa+feb41kAk02D4aAG6Z8tBF+VNZbmtqyRze2ABfCsGUw+E5VZ7SBYIggHVqZIWpzF0D9TJIDhjzQY2a7pcHt29CmmXm1vKZztSvW7uswK0TbB25fiRxDfMxw6Ah6aIKv+qQnh/B/ZikSBbZ+CUhtA5afLXJt9pl9qRx4D3RJQJRWyzUAdQ3aXlWueaiEBpo01p7O2rO0hz5we4ZolvaC3pods1E05GaTnCdzS83z4GsbrPzAlrbXP4/m5tVx+CB7u3RSSElw+za0aRdeu6nd5xpEUsclkyXee5mIswbLLnB7hnSpBwDi1IqULUm/q2tbeuqTrEzNuGdNdnlnV05o0zanNp5/Pqe9yZYvnSdfEty+DW3mowDHAOg96KX7xtvbnp9oyYTHqAchudmDZRe4/UjWpcoAbmzyYzk65xDSU0sKlJ+V00Uy8qATCvJnnHEG2gOaPhV424SNcBLOHwlqqbBeSXD3ORO9v4EwX82QpJcvDTQMsN9pZm1+MnMrJNvqDe8Tki5w+xGG97Tp/3ychIYt5ej28cU7X1R2jLOo7/1L3m+beQVsYtWvMCKhglmLuDXbNT/XCG1F4M3NzF5QEUj2c3+2URpimtLekuBWG3IaqPjDvdrAhg/+rDlMXfXDNfY7URsOtOBisCT3Ab5PqlefzZ3mYNdcHjlFAGo+s/Ty0FptSZ00DFJcqH46xNDHf7l3YqR92TkvjSun0nutgIGBLLtJgphpfClw+4QQD26fqcfE9VmjJSYo+XXQhHDWvtvog0ZpMhD9hP39hqYvRstHH7hTwaBCLzOaq4IzWrKbxNyr5lrctvTUpZaHzuWNf94v8tdyQYRJfgRvN3/MCZMHby45xdvrgPtDRqVU2lLghg+0/yVGyB0mJiBGtlGBv+z4UJLnbe/yWiF1YdsnpZ56Pxf9lJ4gO6p+feDmZamQ81GduDHqY67w0jHOqfX0Kq3esUZ66tT6b/k5bdZQexHHGjzqsqO1UOfXzSA0uX5DwF0D4CVmbvaQSlfSTGZEx4O59NRZ8ccalYx3BgdSDgwFdw7gSzkg1u61XHrqrMyhtRsU398HB8aAG46kYaKtepDH9m7bcsix74nywYHFODAW3FTMO1m01nSxCq/0ITkW+fyWE1pWYl98dg0O5MA9JClFcUPqPGXVSgmbm2/X9JarP/xSyT2FAteQx/hmQQ7kwE0+OVvtdIW7vLd7Cri34i2H1Yr1H+Ma74KiFK86NA7kwE18sc8b3LXQfEgbS8zcS3jLFZNce3WY15SG8DfKrMuBf9nn75FU4W72N3se1Lz+bS9/rD6Qgttv20J2TC4hIbfJXM0Kr/VuxbgPIa79EWPC3ddiRHx3NAcAGSm4/lod3N4bTk5rmiPs7c/Sq4BGc7DiA1o0M2ZnkYrViVcHB8ZzIJ25tU2tVqiwAQMqKSrwWSNmMy4SO45hE4Mcx5SRx70tppqOl4J44ig5kIKbmfs3RlLHUcFZ6aM88F/Z76xcWSLBfg2GK2GFQW0vIS8GsxcYnbdz5hrM38g3cbCWzKGv1uwpce5qlVn5xd7kqL0Tx8pNPfd5gH2tUbq7yqHU7xDrwYSHScoy2YPewCPAfZf4rBnyQmAwfZbUiAA267ZzO6EeIqgOqU7iXZvT+SDqGuD+fzco626tkBdx/yVnT5kfffkMByGkB1oJ/E8cQ7TUSTGj2RDgvmuDv7UWg7AtETPBkg5KtBS0BXb4jGs6BxiU2ep7iUzJ0bXcO7gV118r5KWQ25JprcpTmLWz5mhJ638AbeLiplh6qkb/0+uUUOi41Ckrfa3whzIyoMCz5zUP6cy3c+/YM7h9yGsNz7jOflp68Q2zNqrkoamTGujGnCLSB4Yl7pOufeqcrgofxgw4MWIjS773PiP2v+MiZHtqgtgruL1nfOmTUhBittahk7iWXDarTS/70osryGbvK7cKblKU2Y9uiUM5lA5N/3HiD2aV/EWnIjx7Bbdy45cKeemctSutM9IzyZZS6UCXUmoPTSWnblsFt1TzJXiaOxFFi7BOLeDaI7gV8kK1YTPAUpc/JJF3MrIyU+oM5tx3pjrxMCnYV5xLq/f41hVGJByRbJRb1ae2j+l3QMc+5uzppbguth/futCI3PsS8d6a4FYb2IJb9nxXG2TL0j5s2a5NH+XDqK0N+TUdflJioVdWjsZ0cikQrPme3Hlga9ZnjOaAjf4cI6nz1FvPM3t8zkgnQ3Iv56RjlCfjsE+FlF3uByZpGCkP207MHMvX0uBGS2EPdbZa1iUTjHu0Ufzyh26kvBzibAVgtddaSOvyPhrxLGva7QncuZNExgpg6fJT1sJLNdMJIMyg7H19YnQvo5ubSuY6HCEcusrNH0qhZxRCI2z3cqOrmm+V8PaXBrf6yvOLQQ2QwC8SUHwb6Avxkvj/5a59ff3EktzbjcaEFmkv/fUgo9xGnwzmaA4Ks0nr8hOCBtqsSbAncCuMUBqgU993pz04RZ3V4YwyK26w9yjLzB8BlevwMeBOl/YiaJc14KDNEqzZZ1o1DKwFbu1/ToLSrQ2wxS8BhtmZzf89L3VvSDRjqEZEU5lkLjXy/pd08PD9qMQq9bsvq4GL/1GH8yIgewL3VBAe0nMp4N5slTsxkh3ZB7gx4PZ7tjNbMNv5VFU5coZqAhoQ2vh51m7oALz3dzD9DrunTfz7+sZvbIkmg4ru2+AP/2Mm1xFKvFdgGpK1KF6MwZPXJHOajwYX+IumxCCT8pr+5P8MsKeOHB5TmT5Gxv1uDkgNm3NaiwccnapjaPTlvhM3x4BbwoXgoHb6QYTvpQcADul/zaJDyraVGWPbKpeANsAvfzSPNzu6Tv4YYnJMATftEz/anHHaFQlQ42tJnZfSArJHIQW454jZsGeZbTVrzI1p+wMScjOmhKVtv7cx4PZbO6XC59XGMXkCaBZt11m7wczNxffarrZIQK6851fKez9zprz0g2ifvc13meWhMTY3z2lQyA1YSrKavKdAgHsYQKeWAgSXGJEBh0o4F9wCHDNRmlXnAdcWO0cN5erLTvPqbM7mlPo/xB4dyrsaNrcGu1zWmzQT6pcOUN4W7+MVz48ZND0/NPjkQlnUgXpPXmcf4B4qevPKCQxzwJ1zsvhaKXupC3ASpr5+9+GuXLjO26qlFryUBrefmXNqr3dMaoch8VP3hsSu52T9tflI4MU3jC4ymrwMuK+T54l0PC0OlAC3Px0ypwoLcBpAMAfS5AvZoH2qdBo+8j3pbVXZo7lvje390uD2M3OqybQlhFBnf08Rh672qd5DbPOUJ34Qlfqv5bgnVnjWApq9g1srkVCdOegcMGjb5b7MpDHCWwLcAlxuZk4FkmyyzxulJ2SqXFfyjAdvzlMse1QhMLLXrjcaor528aw0uDX75nwT3tGWzo5p+4h9kwyTzu5qiwbdIbZ52n6vXeh5BqU/Gs1eRrpncCNMnNms8AudDCC48ExqBqRcmlraJaQ5h89ccHvA5VRFCSv1YpbCQfNho1zIiEGCAaJNWL3A5WLl3k5kqyF2c/EhpC7eLAVu7zPIORe7wngCq2Lf11mlT4WZXEPgJzTFPEnzEp7e9F9b34zi7Z7BDaMkyMxQzDx0ImuKbzPSrKWldkMZ+zUrmGYczQW3997mAOfvU8+u01FUts3p5kNgOZvPq7vM3nPPahdfS87c6WDnzZO+gVLAp14+LTXX/xpEpi4a8eBmQOYqAmxetHdw+1H6GuMHMWgBcYoN1TYAzAW31x7a1DWlKw4xJ5hpbjLKvUtmSVuyCOAgbZM9305tEDB0BMyUKwnurjZgmvgNDlK/BIBFcxuSLMNAp5TWKU334C4ZefhfXfYO7lwWUusSuim91zwzF9wzPp19VDPOkstN+9qwtZ1Y5NGeHIc2hgjc+AWK76G3Z3B7J5QX8nQJ3SHY3H3AmHKf2e2gN/ib0qiFnim5wST9MDSddlTz9gxu2Z7eI6yR1DutDsHmHtWpIwqjUZw1muIMGvGZoysKGL9eC5SluLVncMsx5G1r2eA4SK5uhL5rof7Qfjg0tdzXm8HriQHwoV15Bhn55aEDm9bsGdyytz0PfK7vjcafOYs8vLR05RAPlqqKBVEzJ2dCVazXIb66RMLOIu3aK7jl8U1j0vKUlto6yG/low7FC8vC/hIawSJCEh/ZJgf2Cu5t9lbUOjgwggMB7hHMiqLBgS1xIMC9pd6KugYHRnAgwD2CWVE0OLAlDgS4t9RbUdfgwAgOBLhHMCuKBge2xIEA95Z6K+oaHBjBgf8C4nmml5JfGEAAAAAASUVORK5CYII=\" width=\"123.5\" height=\"45\" alt=\"S = Sum[(an+b) u^n/(n*(n+m)*v^n),{n,1,Infinity}]\" style=\"width: 123.5px; height: 45px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.108px 8px; transform-origin: 375.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = JPMsum1(a,b,m,u,v)\r\n  y = sum([v u m b a]);\r\nend","test_suite":"%%\r\na = 4;\r\nb = 9;\r\nm = 1; \r\nu = 5;\r\nv = 9;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 7;\r\nb = 32;\r\nm = 2; \r\nu = 3;\r\nv = 4;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 16.5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 168;\r\nb = 1058;\r\nm = 2; \r\nu = 19;\r\nv = 23;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 617.5;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 19;\r\nb = 81;\r\nm = 3; \r\nu = 2;\r\nv = 3;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 80/3;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 547;\r\nb = 8232;\r\nm = 3; \r\nu = 13;\r\nv = 14;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 13390/3;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 6095;\r\nb = 82944;\r\nm = 4; \r\nu = 11;\r\nv = 12;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 36704.25;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 469711;\r\nb = 9447840;\r\nm = 5; \r\nu = 17;\r\nv = 18;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 3817735.9;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\na = 117585;\r\nb = 705894;\r\nm = 6; \r\nu = 2;\r\nv = 7;\r\nS = JPMsum1(a,b,m,u,v);\r\nS_correct = 593732/15;\r\nassert(abs(S-S_correct)/S_correct \u003c 1e-12)\r\n\r\n%%\r\nfiletext = fileread('JPMsum1.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'switch') || contains(filetext, 'if'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-09T16:09:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2024-06-09T16:09:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-09T02:41:38.000Z","updated_at":"2026-02-01T07:00:29.000Z","published_at":"2024-06-09T02:41:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following sum\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S = Sum[(an+b) u^n/(n*(n+m)*v^n),{n,1,Infinity}]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS = \\\\sum_{n = 1}^\\\\infty \\\\frac{an+b}{n(n+m)} \\\\frac{u^n}{v^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlthough a solution is available for general values of the coefficients, the coefficients are chosen so that a simpler form is possible. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58394,"title":"Integrate a product of gamma functions","description":"Write a function to compute the following integral:\r\n\r\nwhere  and  is the gamma function, the subject of Cody Problem 46025.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.05px; transform-origin: 407px 52.05px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 8px; transform-origin: 152.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 196.5px; height: 44px;\" width=\"196.5\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.55px; text-align: left; transform-origin: 384px 10.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 56px; height: 20px;\" width=\"56\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.842px 8px; transform-origin: 117.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gamma function, the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46025\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46025\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = intGammaProduct(a)\r\n  f = @(x) gamma(1+i*a*x)*gamma(1-i*a*x);\r\n  y = trapz(x,f);\r\nend","test_suite":"%%\r\na = tan(1);\r\nI_correct = 1.008596722571773;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sqrt(2);\r\nI_correct = 1.110720734539592;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = log(3);\r\nI_correct = 1.429800433690064;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = exp(4);\r\nI_correct = 0.028770138289325;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sinh(5);\r\nI_correct = 0.021168845856719;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = asinh(6);\r\nI_correct = 0.630391294450658;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-06-03T19:50:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-03T14:18:04.000Z","updated_at":"2026-01-26T04:29:04.000Z","published_at":"2023-06-03T14:18:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_{-\\\\infty}^\\\\infty \\\\Gamma(1+iax)\\\\Gamma(1-iax) dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei = \\\\sqrt{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Gamma(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gamma function, the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46025\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46025\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59571,"title":"Compute a sum involving the zeta function","description":"Write a function to compute the sum\r\n\r\nfor , where  is the zeta function, the subject of Cody Problems 45939, 45988, and 45997.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.883px 8px; transform-origin: 111.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the sum\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"137.5\" height=\"45\" alt=\"S(x) = sum(zeta(n+1) x^n) for n = 1 to n = inf\" style=\"width: 137.5px; height: 45px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 8px; transform-origin: 10.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18.5\" alt=\"|x| \u003c 1\" style=\"width: 46.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"34\" height=\"18.5\" alt=\"zeta(m)\" style=\"width: 34px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.517px 8px; transform-origin: 157.517px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the zeta function, the subject of Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45939\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45939\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45988\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45988\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45997\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45997\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function S = zetasum(x)\r\n  n = 1:Inf;\r\n  S = sum(zeta(n+1).*x.^n);\r\nend","test_suite":"%%\r\nx = 1/2;\r\nS = zetasum(x);\r\nS_correct = 1.386294361119891;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 2/3;\r\nS = zetasum(x);\r\nS_correct = 2.554818115119273;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 3/4;\r\nS = zetasum(x);\r\nS_correct = 3.650237868474732;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 5/6;\r\nS = zetasum(x);\r\nS_correct = 5.754911840473381;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 7/8;\r\nS = zetasum(x);\r\nS_correct = 7.811276998394322;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 8/9;\r\nS = zetasum(x);\r\nS_correct = 8.83072761223029;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 9/10;\r\nS = zetasum(x);\r\nS_correct = 9.84653927550954;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 10/11;\r\nS = zetasum(x);\r\nS_correct = 10.85964675709217;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%%\r\nx = 11/12;\r\nS = zetasum(x);\r\nS_correct = 11.87068966352595;\r\nassert(abs(S-S_correct)/S_correct\u003c1e-12)\r\n\r\n%% \r\nx = 0.232931374143;\r\nSS = zetasum(zetasum(x));\r\nSS_correct = 1.227707484938568;\r\nassert(abs(SS-SS_correct)/SS_correct\u003c1e-12)\r\n\r\n%%\r\nx = 1./primes(20);\r\ny = sum(arrayfun(@zetasum,x));\r\ny_correct = 3.2640541637441439;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('zetasum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'switch'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-20T17:57:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-20T13:37:10.000Z","updated_at":"2026-03-04T13:56:18.000Z","published_at":"2024-01-20T13:40:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the sum\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S(x) = sum(zeta(n+1) x^n) for n = 1 to n = inf\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(x) = \\\\sum_{n=1}^\\\\infty \\\\zeta(n+1) x^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"|x| \u0026lt; 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e|x| \u0026lt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"zeta(m)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\zeta(m)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the zeta function, the subject of Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45939\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45939\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45988\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45988\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45997\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45997\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45964,"title":"Compute the nth Pythagorean prime","description":"Pythagorean primes have the form p = 4n+1, where n is an integer, and they can be written as the sum of squares of two integers. More information is available at \u003chttps://en.wikipedia.org/wiki/Pythagorean_prime Wikipedia\u003e, \u003chttps://www.youtube.com/watch?v=yu_aqA7mw7E Numberphile\u003e, and the \u003chttps://oeis.org/A002144 Online Encyclopedia of Integer Sequences\u003e. \r\n\r\nCompute the nth Pythagorean prime p and two integers a and b such that p = a^2+b^2","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.3px 7.8px; transform-origin: 109.3px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePythagorean primes have the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 4n+1\" style=\"width: 70px; height: 18px;\" width=\"70\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.9px 7.8px; transform-origin: 24.9px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209.25px 7.8px; transform-origin: 209.25px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is an integer, and they can be written as the sum of squares of two integers. More information is available at\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pythagorean_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=yu_aqA7mw7E\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eNumberphile\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.2333px 7.8px; transform-origin: 27.2333px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A002144\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOnline Encyclopedia of Integer Sequences\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.0167px 7.8px; transform-origin: 42.0167px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.85px 7.8px; transform-origin: 68.85px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth Pythagorean prime \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.2333px 7.8px; transform-origin: 55.2333px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and two integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.2833px 7.8px; transform-origin: 32.2833px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = a^2+b^2\" style=\"width: 72.5px; height: 19px;\" width=\"72.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [pp,a,b] = PythagoreanPrime(n)\r\n  pp = a^2+b^2;\r\nend","test_suite":"%%\r\nn = 1;\r\npp_correct = 5;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 5;\r\npp_correct = 37;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 25;\r\npp_correct = 257;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 125;\r\npp_correct = 1657;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 625;\r\npp_correct = 10313;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 3125;\r\npp_correct = 62497;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 15625;\r\npp_correct = 367229;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-19T01:58:26.000Z","updated_at":"2026-01-19T15:38:08.000Z","published_at":"2020-06-19T02:08:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePythagorean primes have the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 4n+1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 4n+1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer, and they can be written as the sum of squares of two integers. More information is available at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pythagorean_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=yu_aqA7mw7E\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNumberphile\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A002144\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOnline Encyclopedia of Integer Sequences\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth Pythagorean prime \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and two integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = a^2+b^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = a^2+b^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46582,"title":"Find jumping medalists","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 288px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 144px; transform-origin: 407.5px 144px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.308px 7.875px; transform-origin: 377.308px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eKey questions in number theory involve the distribution of prime numbers. For example, the Twin Prime Conjecture states that infinitely many twin primes, or two primes separated by 2, exist. This conjecture has not been proved, and progress is addressed in an interesting \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=vkMXdShDdtY\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003evideo from Numberphile\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.875px; transform-origin: 3.88333px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.983px 7.875px; transform-origin: 374.983px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem deals with the most common gap between primes up to a given number. John Conway dubbed this gap the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/JumpingChampion.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 56.8083px 7.875px; transform-origin: 56.8083px 7.875px; \"\u003ejumping champion\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 324.392px 7.875px; transform-origin: 324.392px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For numbers up to 20, the jumping champion is 2 because it occurs four times (between 3 and 5, 5 and 7, 11 and 13, and 17 and 19.) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 293.708px 7.875px; transform-origin: 293.708px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo me, the jumping champion is somewhat disappointing because 6 dominates until about 1.74\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAAmCAYAAACMJGZuAAACdElEQVRoge2Z7ZGCMBCGnx7owAZsgAqowA6uAzqwBWuwBHuwBWugBe9HsucaIdnNHOLN5Z3J6MCSj4fN7gLQ1NTU1PQp2gFfwBh/c3Zj0s7Afu0JfooOwB24ALf4/0oAk+oYz+t2ec80t9eOAEiDORMgpB7WARPzEP+FvnjdQj0B1jE5PvIHvKiPzaoOGHjElME53kCAlUKULToRvM/b76rqCXdybkssaSQs5hSvHwjx54p9cZeZ8Xbx+JXneHUy9rmaZGJ6UhZYJ+YXILHmTh6YjDvxugVTOxnrTkgQm0hSuPxaYQ3Ktps5LxnvtnB+zyMmST9jYUyZ361g96PdwuAlWeoSCbQWWBJPlgJwp/rKeQ08gy1JtmWRwZ7gsheL8cxkjoXrrLC0V+W8QRZmgSDbrLSu0WhHzyMWWIEJKMsdtsLS8SMXk7RdybMlUVhgTQWbH4l3WYB5QIEdlo4zOQgj9m19xFZTnWMzywLMCwrssHTWtMKSjNnzms0ke2ovledGXb3Lut3PhTlgNaCgDlbuUURnV/EG8cprnOcQz6UAZW1T7OcQr/EUy0+aA1YLCvywSrFD9yewOh5eM7K8eFlLyc4lDUxXu15QUAcr51n6xrnizJra87w1akCBHdak7Lwxa3PpO+gpK1JtmQ3fotTVvXWYlhWWfiGXiyVWu7doLph76rBUNRW8xQMtxeaqymW9WmBbPRuuKkt5UAPMA0u8aykjHvgAr/LUUV5g1u0lyr3PEs/b7O1mTcFpBSZvOKV/a7UsQTx9U5o+vrxdsnBvDChdl36XS1vJI3esUG3/hmo/C/3bz0lNTU1NTU1NTU31+gYmIUCl6G4nbQAAAABJRU5ErkJggg==\" style=\"width: 37.5px; height: 19px;\" width=\"37.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.45px 7.875px; transform-origin: 68.45px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, I will coin another term: the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.025px 7.875px; transform-origin: 56.025px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ejumping medalists\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 266.817px 7.875px; transform-origin: 266.817px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the three most common gaps between primes up to a given number. For numbers up to 20, the gold, silver, and bronze jumping medals (i.e., first, second, and third place) go to 2, 4, and 1, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 336.983px 7.875px; transform-origin: 336.983px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that determines the jumping medalists as well as the maximum gap. Award the medals as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46576-award-medals-to-winners\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46576\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.925px 7.875px; transform-origin: 206.925px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and return an empty vector for any medal that cannot be awarded.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 7.875px; transform-origin: 0px 7.875px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [J1,J2,J3,Jmax] = jumpingMedalists(n)\r\n  % J1, J2, J3 = most, second-most, and third-most common gaps, respectively\r\n  % Jmax = maximum gap \r\n  \r\n  J = f(n);\r\nend","test_suite":"%%\r\nn = 2;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nassert(isempty(J1) \u0026\u0026 isempty(J2) \u0026\u0026 isempty(J3) \u0026\u0026 isempty(Jmax))\r\n\r\n%%\r\nn = 5;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = [1 2];\r\nJmax_correct = 2;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isempty(J2) \u0026\u0026 isempty(J3) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 7;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 2;\r\nJ2_correct = 1;\r\nJmax_correct = 2;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isempty(J3) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 11;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 2;\r\nJ2_correct = [1 4];\r\nJmax_correct = 4;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isempty(J3) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 20;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 2;\r\nJ2_correct = 4;\r\nJ3_correct = 1;\r\nJmax_correct = 4;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 100;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 2;\r\nJ2_correct = [4 6];\r\nJmax_correct = 8;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isempty(J3) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 3141;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 6;\r\nJ2_correct = 4;\r\nJ3_correct = 2;\r\nJmax_correct = 34;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 50011;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 6;\r\nJ2_correct = 2;\r\nJ3_correct = 4;\r\nJmax_correct = 72;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 6021023;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 6;\r\nJ2_correct = 12;\r\nJ3_correct = 2;\r\nJmax_correct = 154;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 12221997;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 6;\r\nJ2_correct = 12;\r\nJ3_correct = 2;\r\nJmax_correct = 154;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n%%\r\nn = 2e8;\r\n[J1,J2,J3,Jmax] = jumpingMedalists(n);\r\nJ1_correct = 6;\r\nJ2_correct = 12;\r\nJ3_correct = 4;\r\nJmax_correct = 248;\r\nassert(isequal(J1,J1_correct) \u0026\u0026 isequal(J2,J2_correct) \u0026\u0026 isequal(J3,J3_correct) \u0026\u0026 isequal(Jmax,Jmax_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-10T02:33:57.000Z","updated_at":"2026-01-20T11:05:32.000Z","published_at":"2020-09-10T04:15:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eKey questions in number theory involve the distribution of prime numbers. For example, the Twin Prime Conjecture states that infinitely many twin primes, or two primes separated by 2, exist. This conjecture has not been proved, and progress is addressed in an interesting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=vkMXdShDdtY\\\"\u003e\u003cw:r\u003e\u003cw:t\u003evideo from Numberphile\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with the most common gap between primes up to a given number. John Conway dubbed this gap the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/JumpingChampion.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ejumping champion\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. For numbers up to 20, the jumping champion is 2 because it occurs four times (between 3 and 5, 5 and 7, 11 and 13, and 17 and 19.) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo me, the jumping champion is somewhat disappointing because 6 dominates until about 1.74\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\times 10^{35}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, I will coin another term: the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ejumping medalists\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, or the three most common gaps between primes up to a given number. For numbers up to 20, the gold, silver, and bronze jumping medals (i.e., first, second, and third place) go to 2, 4, and 1, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that determines the jumping medalists as well as the maximum gap. Award the medals as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46576-award-medals-to-winners\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46576\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and return an empty vector for any medal that cannot be awarded.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60401,"title":"Find primes and integers that solve an equation","description":"Write a function to find all primes  and non-negative integers  that solve the equation\r\n\r\nwhere  is an integer. If there are no solutions for a given value of , return p = [] and k = [].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.333px 8px; transform-origin: 103.333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find all primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.8083px 8px; transform-origin: 84.8083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and non-negative integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 8px; transform-origin: 72.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that solve the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"79.5\" height=\"19\" alt=\"p! + ap = k^2\" style=\"width: 79.5px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 179.692px 8px; transform-origin: 179.692px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is an integer. If there are no solutions for a given value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.1083px 8px; transform-origin: 24.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.95px 8px; transform-origin: 26.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ep = [] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.6167px 8px; transform-origin: 13.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.1px 8px; transform-origin: 23.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek = []\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,k] = Wilson(a)\r\n  p = primes(a); \r\n  k = randi(a);\r\nend","test_suite":"%%\r\na = 25;\r\n[p,k] = Wilson(a);\r\np_correct = 3;\r\nk_correct = 9;\r\nassert(isequal(p,p_correct) \u0026\u0026 isequal(k,k_correct))\r\n\r\n%%\r\na = -4;\r\n[p,k] = Wilson(a);\r\np_correct = 5;\r\nk_correct = 10;\r\nassert(isequal(p,p_correct) \u0026\u0026 isequal(k,k_correct))\r\n\r\n%%\r\na = 7;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str((k*p)^k)-'0');\r\ns_correct = 19;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\na = 10;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str((k*p)^k)-'0');\r\ns_correct = 18;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\na = 17;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str((k*p)^k)-'0');\r\ns_correct = 45;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\na = 21;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str((k*p)^p)-'0');\r\ns_correct = 45;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\na = 31;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str((k*p)^k)-'0');\r\ns_correct = 58;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\na = 12;\r\n[p,k] = Wilson(a);\r\nassert(isempty(p) \u0026\u0026 isempty(k))\r\n\r\n%%\r\na = -20;\r\n[p,k] = Wilson(a);\r\ns = sum(num2str(k^p)-'0');\r\ns_correct = 25;\r\nassert(isequal(s,s_correct))\r\n\r\n%% \r\nA = -[1 2 24];\r\nj = randi(3);\r\n[~,k] = Wilson(A(j));\r\nassert(~k)\r\n\r\n%%\r\na = -19;\r\n[p,k] = Wilson(a);\r\nassert(isequal(p,k))\r\n\r\n%%\r\na = 22;\r\n[p,k] = Wilson(a);\r\nassert(isempty(p) \u0026\u0026 isempty(k))\r\n\r\n%%\r\nfiletext = fileread('Wilson.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-25T05:11:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-25T05:11:40.000Z","updated_at":"2026-02-02T04:13:20.000Z","published_at":"2024-05-25T05:11:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find all primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and non-negative integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that solve the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p! + ap = k^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep! + ap = k^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. If there are no solutions for a given value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep = [] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek = []\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60331,"title":"Compute the area of a Q","description":"A figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \r\nWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 477.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 238.85px; transform-origin: 407px 238.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.408px 8px; transform-origin: 380.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 316.85px 8px; transform-origin: 316.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 166.85px; text-align: left; transform-origin: 384px 166.85px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Qarea(a,c)\r\n  y = a*c;\r\nend","test_suite":"%%\r\na = 1;\r\nc = sqrt(2);\r\ny = Qarea(a,c);\r\ny_correct = 2.121320343559643;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 2;\r\nc = sqrt(5);\r\ny = Qarea(a,c);\r\ny_correct = 5.031152949374527;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 5/2;\r\nc = sqrt(7);\r\ny = Qarea(a,c);\r\ny_correct = 7.011240974321167;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 3;\r\nc = sqrt(8);\r\ny = Qarea(a,c);\r\ny_correct = 8.013876853447540;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 3;\r\nc = sqrt(11);\r\ny = Qarea(a,c);\r\ny_correct = 11.055415967851332;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 4;\r\nc = sqrt(19);\r\ny = Qarea(a,c);\r\ny_correct = 19.070182877990447;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 5;\r\nc = sqrt(23);\r\ny = Qarea(a,c);\r\ny_correct = 23.019991311901052;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = sqrt(27);\r\nc = sqrt(29);\r\ny = Qarea(a,c);\r\ny_correct = 29.018512609609640;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = 6;\r\nc = sqrt(31);\r\ny = Qarea(a,c);\r\ny_correct = 31.086684359134285;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\na = sqrt(43);\r\nc = sqrt(41);\r\ny = Qarea(a,c);\r\ny_correct = 41.011626258563474;\r\nassert(abs(y-y_correct)/y_correct\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('Qarea.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-18T15:50:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-18T03:49:34.000Z","updated_at":"2026-03-04T13:41:21.000Z","published_at":"2024-05-18T03:49:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA figure resembling a Q (as in “quadrature”) is constructed in the following way: A right triangle is drawn with the left vertex at the point (-a,0) and the top vertex at the point (0,c). The centers of five circles, shown with Xs, are located at the midpoints of the upper two sides, the altitude from the top vertex, and the segments from the two bottom vertices to the point where the altitude meets the bottom side. The radii of the five circles are equal to half the length of the respective segments. Then the Q is formed by the four shaded regions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the area of the Q (i.e., the total area of the shaded regions) given a and c. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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an equation involving primes and fractions","description":"Write a function to find pairs of primes  and  satisfying the equation\r\n\r\nwhere  is an integer. The function should take a number  as input and produce the triples , , and  such that . If there are no solutions, the function should return three empty vectors.\r\nThis problem is adapted from one in the 2012 European Girls’ Math Olympiad. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 73px; transform-origin: 343px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find pairs of primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e satisfying the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136\" height=\"35\" alt=\"p/(p+1) + (q+1)/q = 2n/(n+2)\" style=\"width: 136px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer. The function should take a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and produce the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"18\" alt=\"p \u003c= x\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If there are no solutions, the function should return three empty vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis problem is adapted from one in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.egmo2012.org.uk/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e2012 European Girls’ Math Olympiad\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,q,n] = EGMO2012no5(x)\r\n  p = primes(x); q = primes(x); n = p./(p+1) + (q+1)./q; \r\nend","test_suite":"%%\r\nx = 1;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(isempty(p) \u0026\u0026 isempty(q) \u0026\u0026 isempty(n))\r\n\r\n%%\r\nx = 2;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(all(p==2) \u0026\u0026 isequal(q,[5 7]) \u0026\u0026 isequal(n,[28 19]))\r\n\r\n%%\r\nx = 20;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 200;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402 3778 7306 14758 21166 42226 47302 77002 90898 130678 148606 158002];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 2000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 63;\r\nsum_correct = 265170305;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\n\r\n%%\r\nx = 20000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 344;\r\nsum_correct = 150118037395;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2000000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 14873;\r\nsum_correct = 27402595128;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2e8;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 813373;\r\nsum_correct = 152663390088360;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('EGMO2012no5.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-30T13:15:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-30T05:04:32.000Z","updated_at":"2025-12-14T08:06:30.000Z","published_at":"2022-12-30T05:05:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find pairs of primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e satisfying the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p/(p+1) + (q+1)/q = 2n/(n+2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{p}{p+1} + \\\\frac{q+1}{q} = \\\\frac{2n}{n+2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. The function should take a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produce the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p \u0026lt;= x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep \\\\le x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there are no solutions, the function should return three empty vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is adapted from one in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.egmo2012.org.uk/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2012 European Girls’ Math Olympiad\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59521,"title":"Integrate a power tower","description":"Write a function to compute this integral\r\n\r\nwhere . That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52px; transform-origin: 407px 52px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.783px 8px; transform-origin: 122.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute this integral\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"135\" height=\"44\" alt=\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\" style=\"width: 135px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.3px 8px; transform-origin: 226.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = intPowerTower(a)\r\n  I = integral(x^x^x^x^x^x^x^x,0,a);\r\nend","test_suite":"%%\r\na = 0;\r\nI = intPowerTower(a);\r\nassert(abs(I)\u003c1e-6)\r\n\r\n%%\r\na = 1/100;\r\nI = intPowerTower(a);\r\nI_correct = 0.00975627404012066;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/20;\r\nI = intPowerTower(a);\r\nI_correct = 0.04621245261821598;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/10;\r\nI = intPowerTower(a);\r\nI_correct = 0.0886781687569094;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/5;\r\nI = intPowerTower(a);\r\nI_correct = 0.1685639964895788;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.2071658901263798;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/8;\r\nI = intPowerTower(a);\r\nI_correct = 0.30215124860335973;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/2;\r\nI = intPowerTower(a);\r\nI_correct = 0.3972053202401857;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 2/3;\r\nI = intPowerTower(a);\r\nI_correct = 0.5277402852630483;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.5959989560650945;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 5/6;\r\nI = intPowerTower(a);\r\nI_correct = 0.6671963910854818;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1;\r\nI = intPowerTower(a);\r\nI_correct = 0.822467033424113;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = (rand+3)/4;\r\nI = intPowerTower(a);\r\nI_correct = polyval([0.3875275 -0.9886411 1.132527 0.1505356 0.1405179],a);\r\nassert(abs(I-I_correct)\u003c5e-6)\r\n\r\n%%\r\nfiletext = fileread('intPowerTower.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'find') || contains(filetext,'switch'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-03T15:06:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-31T18:50:11.000Z","updated_at":"2026-01-28T06:58:04.000Z","published_at":"2023-12-31T18:50:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute this integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^a {(x^x)^{(x^x)^{(x^x)\\\\ldots}} dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \\\\le a \\\\le 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"group:YouTube-inspired","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"group:YouTube-inspired","current_player":null,"sort":"map(difficulty_value,0,0,999) 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