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%I #9 Feb 26 2022 10:11:00
%S 0,1,2,5,7,11,14,19,23,26,38,55,59,67,71,74,86,103,107,115,119,127,
%T 131,139,143,175,179,187,191,223,227,235,239,266,278,314,326,367,371,
%U 379,383,415,419,427,431,463,467,475,479,506,518,554,566,607,611,619,623
%N Numbers that in factorial-base representation have digits with an alternating parity.
%H Amiram Eldar, <a href="/A351897/b351897.txt">Table of n, a(n) for n = 1..20477</a> (terms below 10!)
%e 7 is a term since its factorial-base representation is 101 and the parities of its digits are odd, even, odd.
%t max = 7; q[n_] := AllTrue[Differences@ Mod[IntegerDigits[n, MixedRadix[Range[max, 2, -1]]], 2], # != 0 &]; Select[Range[0, 1000], q]
%Y Cf. A007623.
%Y Similar sequences: A000975 (binary), A030141 (decimal), A033068 (ternary), A179970 (quaternary).
%Y Subsequences: A033312, A138524, A341900.
%K nonn,base
%O 1,3
%A _Amiram Eldar_, Feb 24 2022
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