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

1,1

Comments

Positions of terms larger than ones in A264990.

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.

Example

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.

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 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A265350 (MATCHING-POS 1 1 (lambda (n) (> (A264990 n) 1))))

Crossrefs

Cf. A007623, A264990.

Cf. A265349 (complement).

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

Sequence in context: A122987 A047530 A346300 * A096315 A286395 A112680

Adjacent sequences: A265347 A265348 A265349 * A265351 A265352 A265353

Keyword

nonn,base

Author

Antti Karttunen, Dec 22 2015

Status

approved