A176787 a(n) = (0!-1!+2!-3!....(-1)^(n-1)*(n-1)!) mod n.

0, 0, 2, 0, 0, 2, 4, 4, 8, 0, 5, 8, 0, 4, 5, 12, 9, 8, 15, 0, 11, 16, 19, 20, 20, 0, 17, 4, 20, 20, 10, 28, 5, 26, 25, 8, 0, 34, 26, 20, 2, 32, 6, 16, 35, 42, 7, 44, 11, 20, 26, 0, 21, 44, 5, 4, 53, 20, 33, 20, 49, 10, 53, 60, 0, 38, 6, 60, 65, 60, 65, 44, 16, 0, 20, 72, 60, 26, 5, 60, 17

Offset

1,3

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = A058006(n) mod n. - R. J. Mathar, Jul 13 2012

Example

a(1) = 0! mod 1 = 1 mod 1 = 0;
a(2) = (0!-1!) mod 2 = (1 - 1) mod 2 = 0;
a(3) = (0!-1!+2!) mod 3 = (1 - 1 + 2) mod 3 = 2.

Maple

A176787 := proc(n): add((-1)^(k-1)*(k-1)!, k=1..n) mod n end: seq(A176787(n), n=1..81); # Johannes W. Meijer, Jun 28 2011

Mathematica

Table[Mod[Sum[(-1)^k*k!, {k, 0, n - 1}], n], {n, 81}] (* Michael De Vlieger, Apr 22 2015 *)

Prog

(PARI) a(n) = sum(k=0, n-1, (-1)^k*k!) % n; \\ Michel Marcus, Apr 22 2015

Crossrefs

Cf. A049782, A064383 (n such that a(n) is 0).

Sequence in context: A028641 A325190 A141416 * A127862 A342223 A223142

Adjacent sequences: A176784 A176785 A176786 * A176788 A176789 A176790

Keyword

nonn

Author

Paolo P. Lava & Giorgio Balzarotti, Apr 26 2010

Extensions

Edited by Johannes W. Meijer, Jun 28 2011

Status

approved