A023259 Primes that remain prime through 2 iterations of function f(x) = 7x + 6.

5, 11, 31, 59, 61, 71, 149, 179, 269, 439, 499, 541, 571, 719, 761, 1049, 1091, 1181, 1319, 1451, 1489, 1579, 1601, 1831, 1861, 1879, 1949, 2069, 2089, 2269, 2311, 2389, 2441, 2621, 2699, 2819, 2851, 2909, 3001, 3079, 3119, 3391, 3529, 3631, 3701, 3709

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 7*p+6 and 49*p+48 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023225, A024900. - John Cerkan, Sep 14 2016

Programs

Magma

[n: n in [1..100000] | IsPrime(n) and IsPrime(7*n+6) and IsPrime(49*n+48)] // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime[Range[600]],AllTrue[Rest[NestList[7#+6&,#,2]],PrimeQ]&] (* Harvey P. Dale, Jan 26 2024 *)

Formula

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