A227149 Numbers k for which the sum of digits is odd when k is written in the factorial base (A007623).

1, 2, 5, 6, 9, 10, 13, 14, 17, 18, 21, 22, 24, 27, 28, 31, 32, 35, 36, 39, 40, 43, 44, 47, 49, 50, 53, 54, 57, 58, 61, 62, 65, 66, 69, 70, 72, 75, 76, 79, 80, 83, 84, 87, 88, 91, 92, 95, 97, 98, 101, 102, 105, 106, 109, 110, 113, 114, 117, 118, 120, 123, 124

Offset: 1

Author

Antti Karttunen, Jul 02 2013

Keywords

• nonn
• base

Comments

Numbers k for which minimal number of factorials needed to add to get k is odd.

This sequence offers one possible analog to A000069 (odious numbers) in factorial base system. A227132 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, A227148.

The sequence gives the positions of odd permutations in the tables A055089 and A195663; and equivalently, the positions of odd numbers in A055091.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2520
• Wikipedia, Parity of permutation.
• Index entries for sequences related to factorial base representation

Crossrefs

Complement: A227148. Cf. also A000069, A034968, A055091, A227132.

Characteristic function: A374468, see also A262725.

Programs

Mathematica

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 *)