%N Numbers k such that k and k+2 both have an equal number of odd and even digits in their factorial-base representations.
%H Amiram Eldar, <a href="/A351896/b351896.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 71 is a term since the factorial-base representations of 71 and 73 are 2321 and 3001, respectively, and both have 2 odd digits and 2 even digits.
%t max = 7; fctBaseDigits[n_] := IntegerDigits[n, MixedRadix[Range[max, 2, -1]]]; s = Select[Range[1, max!], EvenQ[Length[(d = fctBaseDigits[#])]] && Count[d, _?EvenQ] == Length[d]/2 &]; ind = Position[Differences[s], 2] // Flatten; s[[ind]]
%Y Subsequence of A351895.
%Y Cf. A007623, A351893, A351894.
%Y Similar sequence: A337238.
%A _Amiram Eldar_, Feb 24 2022