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

Author

Antti Karttunen, Dec 22 2015

Keywords

• nonn
• base

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.

Examples

			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.
		

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.

Crossrefs

Cf. A007623, A264990.

Cf. A265350 (complement).

Cf. A000142 (a subsequence).

Cf. also A266117.

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]; q[0] = True; Select[Range[0, 260], q] (* Amiram Eldar, Jan 24 2024 *)