A265349 Numbers in whose factorial base representation (A007623) no digit > 0 occurs more than once.

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10080

Indranil Ghosh, Python program for computing this sequence.

Index entries for sequences related to factorial base representation.

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. A007623, A264990.

Cf. A265350 (complement).

Cf. A000142 (a subsequence).

Cf. also A266117.

Sequence in context: A108853 A257085 A334736 * A047433 A287332 A029465

Adjacent sequences: A265346 A265347 A265348 * A265350 A265351 A265352

Keyword

nonn,base

Author

Antti Karttunen, Dec 22 2015

Status

approved