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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).
6
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.
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. A265349 (complement).
Cf. A007489, A046807 (subsequences from 3 onward).
Sequence in context: A122987 A047530 A346300 * A096315 A286395 A112680
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Dec 22 2015
STATUS
approved