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

1,2

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)

Index entries for sequences related to factorial base representation.

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 *)

Prog

(PARI) is_A227157(n) = { my(i=2); while(n, if(!(n%i), return(0)); n = n\i; i++); (1); }; \\ Antti Karttunen, Dec 29 2025
(Scheme) ;; With Antti Karttunen's IntSeq-library.
(define A227157 (NONZERO-POS 1 1 A208575))

Crossrefs

The sequence gives all k for which A208575(k) is not zero. Also numbers k such that A208575(k) = A227153(k).

Complement of A227187. Subsets: A071156 (apart from zero), A231716, A231720.

Cf. also A003422, A007489, A007623, A153880, A227130, A227132, A304036 and A328574 (analogous sequence).

Sequence in context: A047270 A084060 A328574 * A024896 A160771 A249426

Adjacent sequences: A227154 A227155 A227156 * A227158 A227159 A227160

Keyword

nonn,base

Author

Antti Karttunen, Jul 04 2013

Status

approved