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

1,2

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.

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 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library): (define A227149 (MATCHING-POS 1 0 (lambda (i) (odd? (A034968 i)))))

Crossrefs

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

Sequence in context: A133759 A188258 A308395 * A264120 A042963 A327220

Adjacent sequences: A227146 A227147 A227148 * A227150 A227151 A227152

Keyword

nonn,base

Author

Antti Karttunen, Jul 02 2013

Status

approved