A232039 - OEIS

%I #18 Nov 19 2013 13:42:34

%S 109,769,1429,2089,2161,2749,3541,4729,4969,6577,6709,7369,8689,9349,

%T 9613,10009,11329,13309,14629,15289,17029,17929,19249,21757,22549,

%U 23209,23869,24793,25189,25849,30469,33769,34429,35089,39709,41077,42349,43669,46309

%N 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 A prime p is in the sequence if p is of the form 660*n + 109.

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>

%e 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 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 Select[12Range[864] + 1, PrimeQ[#] && Not[Divisible[Numerator[Bernoulli[# + 1]], (# + 1)/2]] &] (* _Alonso del Arte_, Nov 17 2013 *)

%o (PARI) forstep(p=1, 46309, 12, if(isprime(p)&&!Mod(numerator(bernfrac(p+1)), (p+1)/2)==0, print1(p, ", ")));

%Y Cf. A000367, A000928, A068228, A232040.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Nov 17 2013