A265350 Numbers whose factorial base representation (A007623) contains at least one of the nonzero digits occurs more than once (although not necessarily in adjacent positions).

3, 7, 8, 9, 11, 15, 16, 17, 21, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 47, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 69, 70, 71, 75, 79, 80, 81, 83, 87, 88, 89, 90, 91, 92, 93, 94, 95, 99, 103, 104, 105, 107, 111, 112, 113, 117, 121, 122, 123, 125, 126, 127, 128, 129, 130

Offset: 1

Author

Antti Karttunen, Dec 22 2015

Keywords

• nonn
• base

Comments

Positions of terms larger than ones in A264990.

Examples

			For n=7 the factorial base representation (A007623) is "101" as 7 = 3!+1! = 6+1. Digit "1" occurs twice in it, thus 7 is included in this sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080
• Indranil Ghosh, Python program for computing this sequence.
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A007623, A264990.

Cf. A265349 (complement).

Cf. A007489, A046807 (subsequences from 3 onward).

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++]; Max[Tally[Select[s, # > 0 &]][[;;,2]]] > 1]; Select[Range[130], q] (* Amiram Eldar, Jan 24 2024 *)