A227130 Numbers k for which there is an even number of nonzero digits when k is written in the factorial base (A007623).

0, 3, 5, 7, 8, 10, 13, 14, 16, 19, 20, 22, 25, 26, 28, 30, 33, 35, 36, 39, 41, 42, 45, 47, 49, 50, 52, 54, 57, 59, 60, 63, 65, 66, 69, 71, 73, 74, 76, 78, 81, 83, 84, 87, 89, 90, 93, 95, 97, 98, 100, 102, 105, 107, 108, 111, 113, 114, 117, 119, 121, 122, 124

Offset

1,2

Comments

This sequence offers one possible analog to A001969 (evil numbers) in the factorial base system. A227148 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, A227132.

The sequence gives the positions of even 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++]; EvenQ[c]]; Select[Range[0, 150], q] (* Amiram Eldar, Jan 23 2024 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library): (define A227130 (MATCHING-POS 1 0 (lambda (i) (even? (A060130 i)))))

Crossrefs

Complement: A227132. Cf. also A001969, A060130, A227148.

Sequence in context: A191202 A024977 A088759 * A258025 A239419 A195439

Adjacent sequences: A227127 A227128 A227129 * A227131 A227132 A227133

Keyword

nonn,base

Author

Antti Karttunen, Jul 02 2013

Status

approved