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%I #10 Feb 26 2022 10:11:10
%S 1,3,9,21,33,45,81,93,153,165,201,213,393,405,441,453,633,645,681,693,
%T 873,885,921,933,1113,1125,1161,1173,1353,1365,1401,1413,2313,2325,
%U 2361,2373,2553,2565,2601,2613,2793,2805,2841,2853,3753,3765,3801,3813,3993,4005
%N Numbers that contain only odd digits in their factorial-base representation.
%C All the terms above 1 are odd multiples of 3.
%H Amiram Eldar, <a href="/A351894/b351894.txt">Table of n, a(n) for n = 1..18056</a> (terms below 11!)
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system">Factorial number system</a>.
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e 3 is a term since its factorial-base presentation, 11, has only odd digits.
%e 21 is a term since its factorial-base presentation, 311, has only odd digits.
%t max = 7; fctBaseDigits[n_] := IntegerDigits[n, MixedRadix[Range[max, 2, -1]]]; Select[Range[1, max!, 2], AllTrue[fctBaseDigits[#], OddQ] &]
%Y Cf. A007623, A016945, A351893.
%Y Subsequence: A007489
%Y Similar sequences: A003462 \ {0} (ternary), A014261 (decimal), A032911 (base 4), A032912 (base 5), A033032 (base 6), A033033 (base 7), A033034 (base 8), A033035 (base 9), A033036 (base 11), A033037 (base 12), A033038 (base 13), A033039 (base 14), A033040 (base 15), A033041 (base 16), A126646 (binary).
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Feb 24 2022