A071544 Smallest k such that n+k divides (k+1)!-k!.

5, 2, 3, 4, 5, 3, 5, 4, 6, 5, 7, 4, 7, 6, 3, 8, 7, 6, 5, 4, 6, 8, 7, 6, 5, 6, 8, 4, 7, 6, 9, 8, 7, 6, 5, 9, 8, 7, 6, 8, 7, 6, 11, 4, 5, 10, 9, 6, 7, 10, 9, 8, 7, 6, 5, 7, 13, 12, 11, 10, 9, 8, 7, 8, 7, 6, 13, 12, 11, 5, 9, 8, 7, 6, 9, 8, 7, 12, 11, 10, 9, 8, 7, 6, 11, 10, 9, 8, 11, 6, 7, 4, 12, 11, 5

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Mathematica

a[n_]:=Module[{k=1}, While[!Divisible[(k+1)!-k!, n+k], k++]; k]; Array[a, 95] (* Stefano Spezia, Aug 02 2024 *)

Prog

(PARI) a(n) = {k = 1; while (((k+1)! - k!) % (n+k), k++); k; } \\ Michel Marcus, Nov 26 2013
(Magma) a := function(n) k := 1; while (k*Factorial(k)) mod (n+k) ne 0 do k +:= 1; end while; return k; end function;
[ a(n) : n in [1..95] ]; // Vincenzo Librandi, Jan 21 2026

Crossrefs

Cf. A001563.

Sequence in context: A019812 A375080 A222222 * A031285 A307603 A234593

Adjacent sequences: A071541 A071542 A071543 * A071545 A071546 A071547

Keyword

easy,nonn

Author

Benoit Cloitre, May 30 2002

Status

approved