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A232039 Primes p congruent to 1 mod 12 such that (p + 1)/2 does not divide the numerator of the Bernoulli number B(p + 1).

%I A232039 #18 Nov 19 2013 13:42:34
%S A232039 109,769,1429,2089,2161,2749,3541,4729,4969,6577,6709,7369,8689,9349,
%T A232039 9613,10009,11329,13309,14629,15289,17029,17929,19249,21757,22549,
%U A232039 23209,23869,24793,25189,25849,30469,33769,34429,35089,39709,41077,42349,43669,46309
%N A232039 Primes p congruent to 1 mod 12 such that (p + 1)/2 does not divide the numerator of the Bernoulli number B(p + 1).
%C A232039 A prime p is in the sequence if p is of the form 660*n + 109.
%H A232039 <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>
%e A232039 109 is in the sequence because B(110) = (5 * 157 * 76493 * C)/1518 (where C is some large, unfactored composite number), the numerator of which is not divisible by 110/2 = 5 * 11.
%e A232039 97 is not in the sequence because B(98) = (7^2 * 2857 * 3221 * C)/6, the numerator of which is divisible by 98/2 = 49 = 7^2.
%t A232039 Select[12Range[864] + 1, PrimeQ[#] && Not[Divisible[Numerator[Bernoulli[# + 1]], (# + 1)/2]] &] (* _Alonso del Arte_, Nov 17 2013 *)
%o A232039 (PARI) forstep(p=1, 46309, 12, if(isprime(p)&&!Mod(numerator(bernfrac(p+1)), (p+1)/2)==0, print1(p, ", ")));
%Y A232039 Cf. A000367, A000928, A068228, A232040.
%K A232039 nonn
%O A232039 1,1
%A A232039 _Arkadiusz Wesolowski_, Nov 17 2013