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

1,4

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

Mathematica

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

Prog

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

Crossrefs

Cf. A061007.

Sequence in context: A354058 A323878 A046094 * A293305 A316896 A230626

Adjacent sequences: A055973 A055974 A055975 * A055977 A055978 A055979

Keyword

easy,nonn

Author

Robert G. Wilson v, Jul 23 2000

Status

approved