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%I #10 Feb 26 2022 10:11:07
%S 2,5,25,26,29,30,34,37,38,41,42,46,51,55,56,59,63,67,68,71,73,74,77,
%T 78,82,85,86,89,90,94,99,103,104,107,111,115,116,119,723,727,728,731,
%U 735,739,740,743,745,746,749,750,754,757,758,761,762,766,771,775,776
%N Numbers with an equal number of odd and even digits in their factorial-base representation.
%H Amiram Eldar, <a href="/A351895/b351895.txt">Table of n, a(n) for n = 1..10000</a>
%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 5 is a term since its factorial-base representation, 21, has one odd digit, 1, and one even digit, 2.
%t max = 7; fctBaseDigits[n_] := IntegerDigits[n, MixedRadix[Range[max, 2, -1]]]; Select[Range[1, max!], EvenQ[Length[(d = fctBaseDigits[#])]] && Count[d, _?EvenQ] == Length[d]/2 &]
%Y Cf. A007623, A351893, A351894.
%Y A138524 is a subsequence.
%Y Similar sequences: A031443 (binary), A227870 (decimal).
%K nonn,base
%O 1,1
%A _Amiram Eldar_, Feb 24 2022
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