A056051 a(n) = (n-2)! - 1 (mod n).

0, 0, 1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, -1, -1, -1, -1, 0, -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, 0, -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1

Offset: 2

Author

Robert G. Wilson v, Jul 25 2000

Keywords

• easy
• sign

Comments

(n-2)! - 1 is congruent to 0 iff n is a prime and is congruent to -1 iff n is a composite > 4.

Links

• Antti Karttunen, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A005171.

Programs

Mathematica

Do[m = Mod[(n - 2)! - 1, n]; If[m < 2, Print[m], Print[m - n]], {n, 2, 100}]

PARI

A056051(n) = { my(m=(((n-2)!-1)%n)); if(m < 2,m,m-n); }; \\ Antti Karttunen, Sep 14 2017, after Mathematica-code.