A285982 a(n) = n! (mod n + 3).

1, 1, 2, 0, 3, 0, 0, 0, 5, 0, 6, 0, 0, 0, 8, 0, 9, 0, 0, 0, 11, 0, 0, 0, 0, 0, 14, 0, 15, 0, 0, 0, 0, 0, 18, 0, 0, 0, 20, 0, 21, 0, 0, 0, 23, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 29, 0, 30, 0, 0, 0, 0, 0, 33, 0, 0, 0, 35, 0, 36, 0, 0, 0, 0, 0, 39, 0, 0, 0, 41, 0, 0

Offset: 0

Author

Seiichi Manyama, Apr 29 2017

Keywords

• nonn

Comments

Nonzero terms are a(2 * A130290(n) - 2) = A130290(n) for n > 1. - David A. Corneth, Apr 30 2017

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Wikipedia, Wilson's theorem

Crossrefs

Cf. A000142, A061006, A130290.

Programs

Maple

seq(n! mod (n+3), n=0..100); # Robert Israel, Apr 30 2017

PARI

a(n) = n! % (n+3); \\ Michel Marcus, Apr 30 2017

Formula

a(n) = A000142(n) (mod n + 3).

If n > 1 and a(n) > 0, a(n) = n/2 + 1 and n + 3 is a prime.