Problem 55370. Easy Sequences 69: Radix Economy of Factorials

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Radix_economy\"><w:r><w:rPr><w:b/></w:rPr><w:t>Radix Economy</w:t></w:r></w:hyperlink><w:r><w:t> of a number in a particular base is the number of digits needed to express it in that base, multiplied by the base. In functional form we write: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>E(b,N) = b\\  \\cdot \\ C(N_b)</w:t></w:r></w:customXml><w:r><w:t>, where </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>E</w:t></w:r></w:customXml><w:r><w:t> is the radix econony, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>N</w:t></w:r></w:customXml><w:r><w:t>, are the base and number, respectively, and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>C(N_b)</w:t></w:r></w:customXml><w:r><w:t>, is the number of digits of the base-</w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:t> representation of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>N</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b=2</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>N=1000</w:t></w:r></w:customXml><w:r><w:t>, then the radix economy is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>E=20</w:t></w:r></w:customXml><w:r><w:t>:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[    >> E = 2 * length(dec2bin(1000))\n    >> E =\n        20]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given a base </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, and an integer </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, calculate </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F(b,n)=E(b,N)</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>N= n!</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b=3</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=10</w:t></w:r></w:customXml><w:r><w:t>, we have:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[    >> F = 3 * length(dec2base(factorial(10),3))\n    >> F =\n        42]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>----------------</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>NOTE:</w:t></w:r><w:r><w:t> As it is, this problem is quite simple. In fact, a solution is already given for small values of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>. Therefore, to make it a bit interesting, some built-in functions are disabled.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.440000534057617px; 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; white-space: normal; "><div style="block-size: 378px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 65px; 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; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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; "><span style="">The </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Radix_economy"><span style=""><span style="font-weight: 700; ">Radix Economy</span></span></a><span 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; "><span style=""> of a number in a particular base is the number of digits needed to express it in that base, multiplied by the base. In functional form we write: </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="137.5" height="20" style="width: 137.5px; height: 20px;"></span><span 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; "><span style="">, where </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">E</span><span 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; "><span style=""> is the radix econony, </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">b</span><span 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; "><span style=""> and </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">N</span><span 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; "><span style="">, are the base and number, respectively, and </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="41" height="20" style="width: 41px; height: 20px;"></span><span 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; "><span style="">, is the number of digits of the base-</span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">b</span><span 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; "><span style=""> representation of </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">N</span><span 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; "><span style="">.</span></span></div><div 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; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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; "><span style="">For example, if </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="36.5" height="18" style="width: 36.5px; height: 18px;"></span><span 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; "><span style=""> and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="64" height="18" style="width: 64px; height: 18px;"></span><span 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; "><span style="">, then the radix economy is </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="47.5" height="18" style="width: 47.5px; height: 18px;"></span><span 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; "><span style="">:</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; 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; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    &gt;&gt; E = 2 * length(dec2bin(1000))</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; 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; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    &gt;&gt; E =</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; 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; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">        20</span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span 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; "><span style="font-weight: 700; ">Given a base </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">b</span><span 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; "><span style="font-weight: 700; ">, and an integer </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</span><span 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; "><span style="font-weight: 700; ">, calculate </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="113.5" height="19" style="width: 113.5px; height: 19px;"></span><span 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; "><span style="font-weight: 700; ">, for </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="46.5" height="18" style="width: 46.5px; height: 18px;"></span><span 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; "><span style="font-weight: 700; ">.</span></span></div><div 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; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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; "><span style="">For example, if </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="36.5" height="18" style="width: 36.5px; height: 18px;"></span><span 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; "><span style=""> and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="44" height="18" style="width: 44px; height: 18px;"></span><span 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; "><span style="">, we have:</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; 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; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    &gt;&gt; F = 3 * length(dec2base(factorial(10),3))</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; 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; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    &gt;&gt; F =</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; 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; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; tab-size: 4; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">        42</span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span 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; "><span style="">----------------</span></span></div><div 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; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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; "><span style="font-weight: 700; ">NOTE:</span></span><span 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; "><span style=""> As it is, this problem is quite simple. In fact, a solution is already given for small values of </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">b</span><span 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; "><span style=""> and </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</span><span 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; "><span style="">. Therefore, to make it a bit interesting, some built-in functions are disabled.</span></span></div></div></div>

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Solution 8980740

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Ramon Villamangca on 31 Aug 2022

Almost... This is in the right direction...

Ramy Salem on 31 Aug 2022

@Ramon I don't know how to apply a recursive function to an array
Thus I am failing tests 6 and 7

Ramon Villamangca on 31 Aug 2022

Hi Ramy,

Try to include the array as argument to your recursive call.

Ramy Salem on 31 Aug 2022

Hey Ramon,
Found a work around for the array but I still fail test 7 because the factorial(1234) is just too big so I think my whole methodology is incorrect

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Problem 55370. Easy Sequences 69: Radix Economy of Factorials

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