A046094 - OEIS

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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

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OFFSET

1,9

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.

FORMULA

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

EXAMPLE

- 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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A228037.

Sequence in context: A318513 A354058 A323878 * A055976 A293305 A316896

Adjacent sequences: A046091 A046092 A046093 * A046095 A046096 A046097

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

EXTENSIONS

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

STATUS

approved