A023258 Primes that remain prime through 2 iterations of function f(x) = 6x + 7.

5, 17, 29, 37, 89, 127, 199, 229, 269, 347, 359, 379, 397, 499, 769, 809, 929, 947, 977, 1049, 1087, 1129, 1277, 1279, 1367, 1409, 1439, 1489, 1499, 1607, 1609, 1787, 2017, 2039, 2089, 2399, 2539, 2707, 2819, 2837, 2957, 3089, 3109, 3217, 3229, 3389, 3499

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 6*p+7 and 36*p+49 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023222, A153218. - John Cerkan, Sep 14 2016

Programs

Magma

[n: n in [1..100000] | IsPrime(n) and IsPrime(6*n+7) and IsPrime(36*n+49)] // Vincenzo Librandi, Aug 04 2010

Mathematica

nrpQ[n_]:=AllTrue[Rest[NestList[6#+7&,n,2]],PrimeQ]; Select[Prime[ Range[ 500]],nrpQ] (* Harvey P. Dale, Oct 12 2020 *)

Formula

a(n) = 7 or 9 (mod 10) for n > 1. - John Cerkan, Sep 14 2016