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

Author

Antti Karttunen, Jul 02 2013

Keywords

• nonn
• base

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.

Crossrefs

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

Programs

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 *)