

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).


1



109, 769, 1429, 2089, 2161, 2749, 3541, 4729, 4969, 6577, 6709, 7369, 8689, 9349, 9613, 10009, 11329, 13309, 14629, 15289, 17029, 17929, 19249, 21757, 22549, 23209, 23869, 24793, 25189, 25849, 30469, 33769, 34429, 35089, 39709, 41077, 42349, 43669, 46309
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OFFSET

1,1


COMMENTS

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


LINKS



EXAMPLE

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.
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.


MATHEMATICA

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


PROG

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



