A228037 Odd-indexed terms of Agoh's congruence A046094: a(n) is conjectured to be 1 iff 2n+1 is prime.

0, 1, 1, 1, 3, 1, 1, 5, 1, 1, 7, 1, 5, 9, 1, 1, 11, 0, 1, 13, 1, 1, 24, 1, 7, 17, 1, 0, 19, 1, 1, 21, 13, 1, 23, 1, 1, 25, 0, 1, 27, 1, 17, 29, 1, 13, 31, 0, 1, 33, 1, 1, 56, 1, 1, 37, 1, 0, 39, 0, 11, 41, 25, 1, 43, 1, 19, 45, 1, 1, 47, 0, 29, 49, 1, 1, 51, 0, 1, 53, 0, 1, 88, 1, 13, 57, 1, 25, 59, 1, 1, 61, 37, 0, 63, 1, 1, 65, 1

Offset: 0

Author

Jonathan Sondow, Aug 13 2013

Keywords

• nonn

Comments

Except for A046094(2) = 1, the even-indexed terms of A046094 are all zero since Bernoulli(2n+1) = 0 for n > 0.

Examples

			-(2*1+1)*Bernoulli(2*1) = -3*(1/6) = -1/2 == -2 == 1 mod 3, so a(1) = 1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

a(n) = A046094(2n+1).

Programs

Maple

a:= n-> -(2*n+1)*bernoulli(2*n) mod (2*n+1):
seq(a(n), n=0..100);  # Alois P. Heinz, Aug 13 2013

Mathematica

a[ n_ ] := Mod[ Numerator[ -(2 n + 1)* BernoulliB[ 2 n]] * PowerMod[ Denominator[(2 n + 1)* BernoulliB[ 2 n]], -1, 2 n + 1], 2 n + 1]

Formula

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