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%I #23 Jan 24 2024 01:49:16
%S 1,2,5,6,9,10,13,14,17,18,21,22,24,27,28,31,32,35,36,39,40,43,44,47,
%T 49,50,53,54,57,58,61,62,65,66,69,70,72,75,76,79,80,83,84,87,88,91,92,
%U 95,97,98,101,102,105,106,109,110,113,114,117,118,120,123,124
%N Numbers k for which the sum of digits is odd when k is written in the factorial base (A007623).
%C Numbers k for which minimal number of factorials needed to add to get k is odd.
%C This sequence offers one possible analog to A000069 (odious numbers) in factorial base system. A227132 gives another kind of analog.
%C 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, A227148.
%C The sequence gives the positions of odd permutations in the tables A055089 and A195663; and equivalently, the positions of odd numbers in A055091.
%H Antti Karttunen, <a href="/A227149/b227149.txt">Table of n, a(n) for n = 1..2520</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Parity_of_a_permutation">Parity of permutation</a>.
%t q[n_] := Module[{k = n, m = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, s += r; m++]; OddQ[s]]; Select[Range[125], q] (* _Amiram Eldar_, Jan 24 2024 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library): (define A227149 (MATCHING-POS 1 0 (lambda (i) (odd? (A034968 i)))))
%Y Complement: A227148. Cf. also A000069, A034968, A055091, A227132.
%K nonn,base
%O 1,2
%A _Antti Karttunen_, Jul 02 2013
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