A046094 Agoh's congruence; a(n) is conjectured to be 1 iff n is prime.

0, 1, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 5, 0, 1, 0, 1, 0, 7, 0, 1, 0, 5, 0, 9, 0, 1, 0, 1, 0, 11, 0, 0, 0, 1, 0, 13, 0, 1, 0, 1, 0, 24, 0, 1, 0, 7, 0, 17, 0, 1, 0, 0, 0, 19, 0, 1, 0, 1, 0, 21, 0, 13, 0, 1, 0, 23, 0, 1, 0, 1, 0, 25, 0, 0, 0, 1, 0, 27, 0, 1, 0, 17, 0, 29, 0, 1, 0, 13, 0, 31, 0, 0, 0, 1, 0

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Examples

			- 21 * Bernoulli(20) = 21 * 174611 / 330 = 1222277 / 110  and 1 / 110 == 17 mod 21, so a(21) = 1222277 * 17 mod 21 = 7. - _Jonathan Sondow_, Aug 13 2013
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• D. Borwein, J. M. Borwein, P. B. Borwein and R. Girgensohn, Giuga's conjecture on primality, The American Mathematical Monthly, Vol. 103, No. 1 (1996), 40-50.
• Romeo Meštrović, Generalizations of Carmichael numbers I, arXiv:1305.1867v1 [math.NT], May 4, 2013.
• R. Mestrovic, On a Congruence Modulo n^3 Involving Two Consecutive Sums of Powers, Journal of Integer Sequences, Vol. 17 (2014), 14.8.4.
• Eric Weisstein's World of Mathematics, Agoh's Conjecture
• Index entries for sequences related to Bernoulli numbers.

Crossrefs

Cf. A228037.

Programs

Mathematica

a[ n_ ] := Mod[ Numerator[ -n* BernoulliB[ n-1 ]]*PowerMod[ Denominator[ n*BernoulliB[ n-1 ] ], -1, n ], n ] (* Jonathan Sondow, Aug 13 2013 *)

PARI

a(n) = -n*bernfrac(n-1) % n; \\ Michel Marcus, Aug 08 2017

Formula

a(n) = - n*Bernoulli(n-1) mod n.

Extensions

a(21), a(51), a(57), a(65), a(81) corrected by Jonathan Sondow, Aug 13 2013