A023256 Primes that remain prime through 2 iterations of function f(x) = 6x + 1.

2, 17, 47, 61, 101, 131, 151, 331, 367, 461, 607, 751, 937, 971, 1151, 1321, 1327, 1361, 1481, 1511, 1607, 1811, 1847, 1907, 2081, 2287, 2347, 2357, 2791, 2851, 2971, 3251, 3257, 3457, 3491, 3581, 3761, 4007, 4091, 4127, 4861, 4967, 5231, 5347, 5387, 5407

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 6*p+1 and 36*p+7 are also primes. - Vincenzo Librandi, Aug 04 2010

Subsequence of A007693. - Michel Marcus, Oct 17 2015

Links

• John Cerkan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007693 (1 iteration), A023287 (3 iterations).

Programs

Magma

[n: n in [0..100000] | IsPrime(n) and IsPrime(6*n+1) and IsPrime(36*n+7)] // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime[Range[800]],AllTrue[Rest[NestList[6#+1&,#,2]],PrimeQ]&] (* Harvey P. Dale, Oct 17 2020 *)

PARI

lista(nn) = forprime(n=1, nn, if (isprime(p=6*n+1) && isprime(6*p+1), print1(n, ", "))); \\ Michel Marcus, Oct 17 2015

Formula

a(n) == 1 or 7 (mod 10) for n > 1. - John Cerkan, Sep 14 2016