A227132 Numbers k for which there is an odd number of nonzero digits when k is written in the factorial base (A007623).

1, 2, 4, 6, 9, 11, 12, 15, 17, 18, 21, 23, 24, 27, 29, 31, 32, 34, 37, 38, 40, 43, 44, 46, 48, 51, 53, 55, 56, 58, 61, 62, 64, 67, 68, 70, 72, 75, 77, 79, 80, 82, 85, 86, 88, 91, 92, 94, 96, 99, 101, 103, 104, 106, 109, 110, 112, 115, 116, 118, 120, 123, 125

Offset

1,2

Comments

This sequence offers one possible analog to A000069 (odious numbers) in the factorial base system. A227149 gives another kind of analog.

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.

The sequence gives the positions of odd permutations in the tables A060117 and A060118.

Links

Antti Karttunen, Table of n, a(n) for n = 1..2520

Wikipedia, Parity of permutation.

Mathematica

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 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library): (define A227132 (MATCHING-POS 1 0 (lambda (i) (odd? (A060130 i)))))

Crossrefs

Complement: A227130.

Cf. A007623, A060117, A060118.

Cf. also A000069, A060130, A227149.

Sequence in context: A338348 A184978 A333231 * A024978 A191194 A191231

Adjacent sequences: A227129 A227130 A227131 * A227133 A227134 A227135

Keyword

nonn,base

Author

Antti Karttunen, Jul 02 2013

Status

approved