A055976 Remainder when (n-1)! + 1 is divided by n.

0, 0, 0, 3, 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, 1, 1, 1, 0, 1, 1, 1

Offset: 1

Author

Robert G. Wilson v, Jul 23 2000

Keywords

• easy
• nonn

Comments

Related to Wilson's theorem. a(n) = 0 iff n = 1 or a prime; a(n) = 1 iff n > 4 is composite; a(n) = 3 iff n = 4.

References

• Albert H. Beiler, Recreations in The Theory of Numbers, The Queen of Mathematics Entertains, Second Edition, Dover Publications, Inc., New York, 1966, Page 50.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061007.

Programs

Mathematica

Do[Print[Mod[(n-1)!+1, n]], {n, 1, 100}]

PARI

A055976(n) = (((n-1)!+1)%n); \\ Antti Karttunen, Aug 27 2017