A227157 Numbers k whose factorial base representation A007623(k) does not contain any nonleading zeros.

1, 3, 5, 9, 11, 15, 17, 21, 23, 33, 35, 39, 41, 45, 47, 57, 59, 63, 65, 69, 71, 81, 83, 87, 89, 93, 95, 105, 107, 111, 113, 117, 119, 153, 155, 159, 161, 165, 167, 177, 179, 183, 185, 189, 191, 201, 203, 207, 209, 213, 215, 225, 227, 231, 233, 237, 239, 273

Offset: 1

Author

Antti Karttunen, Jul 04 2013

Keywords

• nonn
• base

Comments

a(A003422(n)) = A007489(n).

a(A007489(n)) = (n+1)!-1 thus A007489(n) gives the number of terms less than (n+1)! in this sequence.

Equivalently, there are n! terms in the sequence with their magnitude in range n!..(n+1)!.

Also numbers k such that A304036(k) = 1 for k > 0. - Seiichi Manyama, May 06 2018

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..5913 from Antti Karttunen)

Crossrefs

The sequence gives all n for which A208575(n) is not zero. Complement of A227187. Subsets: A071156 (apart from zero), A231716, A231720.

Cf. also A003422, A007489, A007623, A153880, A227130, A227132, A304036.

Programs

Mathematica

q[n_] := Module[{k = n, m = 2, c = 0, r}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, If[r == 0, c++]; m++]; c == 0]; Select[Range[300], q] (* Amiram Eldar, Jan 23 2024 *)