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

%I A228037 #23 Dec 11 2019 07:31:21
%S A228037 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,
%T A228037 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,
%U A228037 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
%N A228037 Odd-indexed terms of Agoh's congruence A046094: a(n) is conjectured to be 1 iff 2n+1 is prime.
%C A228037 Except for A046094(2) = 1, the even-indexed terms of A046094 are all zero since Bernoulli(2n+1) = 0 for n > 0.
%H A228037 Alois P. Heinz, <a href="/A228037/b228037.txt">Table of n, a(n) for n = 0..10000</a>
%F A228037 a(n) = - (2n+1)*Bernoulli(2n) mod 2n+1.
%e A228037 -(2*1+1)*Bernoulli(2*1) = -3*(1/6) = -1/2 == -2 == 1 mod 3, so a(1) = 1.
%p A228037 a:= n-> -(2*n+1)*bernoulli(2*n) mod (2*n+1):
%p A228037 seq(a(n), n=0..100);  # _Alois P. Heinz_, Aug 13 2013
%t A228037 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]
%Y A228037 a(n) = A046094(2n+1).
%K A228037 nonn
%O A228037 0,5
%A A228037 _Jonathan Sondow_, Aug 13 2013