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

Author

Paolo P. Lava & Giorgio Balzarotti, Apr 26 2010

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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

Extensions

Edited by Johannes W. Meijer, Jun 28 2011