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A265349
Numbers in whose factorial base representation (A007623) no digit > 0 occurs more than once.
8
0, 1, 2, 4, 5, 6, 10, 12, 13, 14, 18, 19, 20, 22, 23, 24, 28, 36, 42, 46, 48, 49, 50, 54, 66, 67, 68, 72, 73, 74, 76, 77, 78, 82, 84, 85, 86, 96, 97, 98, 100, 101, 102, 106, 108, 109, 110, 114, 115, 116, 118, 119, 120, 124, 132, 138, 142, 168, 186, 192, 196, 204, 216, 220, 228, 234, 238, 240, 241, 242, 246, 258, 259, 260
OFFSET
0,3
COMMENTS
Zero is a special case in this sequence, thus a(0) = 0, and the indexing of natural numbers >= 1 present starts from a(1) = 1.
After a(0), positions of ones in A264990.
EXAMPLE
23 (in factorial base "321") is present, because none of the digits (which all are nonzero) occurs twice.
48 (in factorial base "2000") is present, because the only nonzero digit, "2", occurs only once.
259 (in factorial base "20301") is present, because none of the nonzero digits occurs more than once.
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]; q[0] = True; Select[Range[0, 260], q] (* Amiram Eldar, Jan 24 2024 *)
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(define A265349 (MATCHING-POS 0 0 (lambda (n) (<= (A264990 n) 1))))
CROSSREFS
Cf. A265350 (complement).
Cf. A000142 (a subsequence).
Cf. also A266117.
Sequence in context: A108853 A257085 A334736 * A047433 A287332 A029465
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Dec 22 2015
STATUS
approved