A245056 - OEIS

%I #23 Sep 08 2022 08:46:08

%S 2,109,157,167,197,211,227,317,337,349,353,389,421,439,449,457,521,

%T 541,547,563,571,587,599,613,617,647,677,701,733,757,769,821,823,827,

%U 857,859,877,881,967,977,983,991,1097,1153,1163,1187,1217,1231,1237,1249

%N Primes in the sequence A249134/12.

%C a(n) is in the sequence if Bernoulli number B(12*a(n)) has denominator 2730 and a(n) is prime.

%C 2 together with primes p such that 2p+1, 4p+1, 6p+1, and 12p+1 are all composite. - _Charles R Greathouse IV_, Oct 22 2014

%H Vaclav Kotesovec and Charles R Greathouse IV, <a href="/A245056/b245056.txt">Table of n, a(n) for n = 1..10000</a> (first 385 terms from Kotesovec)

%F a(n) ~ n log n. - _Charles R Greathouse IV_, Oct 22 2014

%t Reap[For[n = 0, n <= 10^4, n = n + 12, If[Denominator[BernoulliB[n]] == 2730 && PrimeQ[n/12], Print[n/12]; Sow[n/12]]]][[2, 1]]

%t Flatten[{2, Select[Table[Prime[k], {k, 300}], Not[PrimeQ[2*# + 1]] && Not[PrimeQ[4*# + 1]] && Not[PrimeQ[6*# + 1]] && Not[PrimeQ[12*# + 1]] &]}] (* _Vaclav Kotesovec_, Aug 03 2019 *)

%o (PARI) is(n)=n==2 || (isprime(n) && !isprime(2*n+1) && !isprime(4*n+1) && !isprime(6*n+1) && !isprime(12*n+1)) \\ _Charles R Greathouse IV_, Oct 22 2014

%o (Magma) [2] cat [n: n in [0..1500] | IsPrime(n) and not IsPrime(2*n+1) and not IsPrime(4*n+1) and not IsPrime(6*n+1) and not IsPrime(12*n+1)]; // _Vincenzo Librandi_, Oct 23 2014

%Y Cf. A249134, A027642, A002445.

%K nonn,easy

%O 1,1

%A _Vaclav Kotesovec_, Oct 22 2014