# Problem 44375. Missing five

Convert decimal numbers to a base-9 notation missing the digit 5

Too many five-themed problems? Wondering whether everything would be simpler if we just got rid of the digit 5? Let's try!

In a world without 5's, positive integers may be represented using a base-9 notation that uses only the digits 0, 1, 2, 3, 4, 6, 7, 8, and 9. We'll call this the "missing-5" notation. The following list shows the first 100 positive numbers (i.e. 1 through 100) using "missing-5" notation:

```    '1'      '2'      '3'      '4'      '6'      '7'      '8'      '9'      '10'     '11'
'12'     '13'     '14'     '16'     '17'     '18'     '19'     '20'     '21'     '22'
'23'     '24'     '26'     '27'     '28'     '29'     '30'     '31'     '32'     '33'
'34'     '36'     '37'     '38'     '39'     '40'     '41'     '42'     '43'     '44'
'46'     '47'     '48'     '49'     '60'     '61'     '62'     '63'     '64'     '66'
'67'     '68'     '69'     '70'     '71'     '72'     '73'     '74'     '76'     '77'
'78'     '79'     '80'     '81'     '82'     '83'     '84'     '86'     '87'     '88'
'89'     '90'     '91'     '92'     '93'     '94'     '96'     '97'     '98'     '99'
'100'    '101'    '102'    '103'    '104'    '106'    '107'    '108'    '109'    '110'
'111'    '112'    '113'    '114'    '116'    '117'    '118'    '119'    '120'    '121'```

You may notice that this is simply the sorted list of positive numbers which do not contain the digit 5 in their decimal representation.

Your function should convert a positive decimal number N into its "missing-5" notation. For example

` dec2missing5(20)`

should return '22' (the 20th positive number in missing-5 notation), and

` dec2missing5(100)`

should return '121' (the 100th positive number in missing-5 notation)

Good luck!

Small print: Your function may output a number, a char array, or a string; whatever you find simpler (e.g. in the example above, valid outputs are 121, '121', or "121"). Input numbers in testsuite are always relatively low valued positive integers (<10,000)

### Solution Stats

28.37% Correct | 71.63% Incorrect
Last Solution submitted on Jul 18, 2024