A235140 Numerator(m*Bernoulli(m-1)+1) (mod m), for m = 1, 3, 5, 7, 9, ...

0, 0, 0, 0, 7, 0, 0, 7, 0, 0, 12, 0, 16, 11, 0, 0, 16, 6, 0, 15, 0, 0, 22, 0, 8, 5, 0, 28, 24, 0, 0, 23, 11, 0, 56, 0, 0, 27, 30, 0, 71, 0, 63, 31, 0, 69, 36, 6, 0, 35, 0, 0, 50, 0, 0, 99, 0, 42, 44, 6, 72, 43, 106, 0, 84, 0, 1, 47, 0, 0, 91, 6, 36, 51, 0, 0, 112, 138, 0, 55, 102, 0, 78, 0, 115, 136, 0, 79, 67, 0, 0, 63, 23, 42, 136, 0, 0, 67, 0, 0, 111

Offset

0,5

Comments

a(n) = numerator((2*n+1)*Bernoulli(2*n)+1) (mod 2*n+1), for n = 0, 1, 2, 3, ...

The Agoh-Giuga Conjecture is that a(n)=0 iff 2*n+1 is 1 or a prime.

Links

Table of n, a(n) for n=0..100.

MathWorld, Giuga's Conjecture

Wikipedia, Agoh-Giuga conjecture

Formula

a(n) = 0 iff A235363(n) = 0.

Mathematica

Table[ Mod[ Numerator[ n*BernoulliB[n - 1] + 1], n], {n, 1, 201, 2}]

Crossrefs

Cf. A007850, A046094, A204187, A228037, A235363.

Sequence in context: A067840 A132712 A021592 * A249119 A154102 A344785

Adjacent sequences: A235137 A235138 A235139 * A235141 A235142 A235143

Keyword

nonn

Author

Jonathan Sondow, Jan 07 2014

Status

approved