This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A227132 #20 Jan 24 2024 01:49:01
%S A227132 1,2,4,6,9,11,12,15,17,18,21,23,24,27,29,31,32,34,37,38,40,43,44,46,
%T A227132 48,51,53,55,56,58,61,62,64,67,68,70,72,75,77,79,80,82,85,86,88,91,92,
%U A227132 94,96,99,101,103,104,106,109,110,112,115,116,118,120,123,125
%N A227132 Numbers k for which there is an odd number of nonzero digits when k is written in the factorial base (A007623).
%C A227132 This sequence offers one possible analog to A000069 (odious numbers) in the factorial base system. A227149 gives another kind of analog.
%C A227132 In each range [0,n!-1] exactly half of the integers are found in this sequence, and the other half of them are found in the complement, A227130.
%C A227132 The sequence gives the positions of odd permutations in the tables A060117 and A060118.
%H A227132 Antti Karttunen, <a href="/A227132/b227132.txt">Table of n, a(n) for n = 1..2520</a>
%H A227132 Wikipedia, <a href="http://en.wikipedia.org/wiki/Parity_of_a_permutation">Parity of permutation</a>.
%t A227132 q[n_] := Module[{k = n, m = 2, c = 0, r}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, If[r != 0, c++]; m++]; OddQ[c]]; Select[Range[150], q] (* _Amiram Eldar_, Jan 24 2024 *)
%o A227132 (Scheme, with _Antti Karttunen_'s IntSeq-library): (define A227132 (MATCHING-POS 1 0 (lambda (i) (odd? (A060130 i)))))
%Y A227132 Complement: A227130.
%Y A227132 Cf. A007623, A060117, A060118.
%Y A227132 Cf. also A000069, A060130, A227149.
%K A227132 nonn,base
%O A227132 1,2
%A A227132 _Antti Karttunen_, Jul 02 2013