A227187 Numbers n whose factorial base representation A007623(n) contains at least one nonleading zero. (Zero is also included as a(0)).

0, 2, 4, 6, 7, 8, 10, 12, 13, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 40, 42, 43, 44, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 60, 61, 62, 64, 66, 67, 68, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 84, 85, 86, 88, 90, 91

Offset: 0

Author

Antti Karttunen, Jul 04 2013

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to factorial base representation.

Crossrefs

Complement: A227157.

The sequence gives all positions n where A208575 is zero and all terms where A257510 (also A257260) are nonzeros.

Cf. A232745 (a subsequence), A232744.

Cf. also A007623, A132371, A153880, A227130, A227132, A256450 (numbers with at least one 1 in their factorial representation).

Programs

Mathematica

q[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; MemberQ[s, 0]]; q[0] = True; Select[Range[0, 100], q] (* Amiram Eldar, Feb 07 2024 *)

Formula

a(0) = 0, a(1) = 2, and for n > 1, if a(n-1) is odd or A257510(a(n-1)) > 1, then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1) + 2. - Antti Karttunen, Apr 29 2015

Other identities:

For all n >= 2, a(A132371(n)) = A000142(n) = n! [See comments in A227157.]