A245056 Primes in the sequence A249134/12.

2, 109, 157, 167, 197, 211, 227, 317, 337, 349, 353, 389, 421, 439, 449, 457, 521, 541, 547, 563, 571, 587, 599, 613, 617, 647, 677, 701, 733, 757, 769, 821, 823, 827, 857, 859, 877, 881, 967, 977, 983, 991, 1097, 1153, 1163, 1187, 1217, 1231, 1237, 1249

Offset: 1

Author

Vaclav Kotesovec, Oct 22 2014

Keywords

• nonn
• easy

Comments

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

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

Links

• Vaclav Kotesovec and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 385 terms from Kotesovec)

Crossrefs

Cf. A249134, A027642, A002445.

Programs

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

Mathematica

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]]
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 *)

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

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Oct 22 2014