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

Author

Jonathan Sondow, Jan 07 2014

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 0..6070
• Eric Weisstein's World of Mathematics, Giuga's Conjecture
• Wikipedia, Agoh-Giuga conjecture

Crossrefs

Cf. A004611, A007850, A046094, A204187, A228037, A235363.

Programs

Maple

seq(numer(m*bernoulli(m-1)+1) mod m, m = 1 .. 300, 2); # Robert Israel, Nov 07 2024

Mathematica

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

Formula

a(n) = numerator((2*n+1)*Bernoulli(2*n)+1) (mod 2*n+1).

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

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

Conjecture: a(n) = (2*n + 7)/3 if n > 1 is in A004611. - Robert Israel, Nov 07 2024