A227148 - OEIS

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A227148

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

0, 3, 4, 7, 8, 11, 12, 15, 16, 19, 20, 23, 25, 26, 29, 30, 33, 34, 37, 38, 41, 42, 45, 46, 48, 51, 52, 55, 56, 59, 60, 63, 64, 67, 68, 71, 73, 74, 77, 78, 81, 82, 85, 86, 89, 90, 93, 94, 96, 99, 100, 103, 104, 107, 108, 111, 112, 115, 116, 119, 121, 122, 125

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

This sequence offers one possible analog to A001969 (evil numbers) in factorial base system. A227130 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, A227149.

The sequence gives the positions of even permutations in the tables A055089 and A195663; and equivalently, the positions of even 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++]; EvenQ[s]]; Select[Range[0, 125], q] (* Amiram Eldar, Jan 24 2024 *)

PROG

(Scheme, with Antti Karttunen's IntSeq-library): (define A227148 (MATCHING-POS 1 0 (lambda (i) (even? (A034968 i)))))

CROSSREFS

Complement: A227149. Cf. also A001969, A034968, A227130.

Sequence in context: A327221 A014601 A154708 * A026444 A003171 A028970

Adjacent sequences: A227145 A227146 A227147 * A227149 A227150 A227151

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Jul 02 2013

STATUS

approved