A023261 Primes that remain prime through 2 iterations of function f(x) = 8x + 3.

5, 13, 31, 61, 101, 103, 163, 191, 233, 241, 251, 433, 461, 643, 751, 761, 821, 863, 983, 1021, 1153, 1193, 1283, 1291, 1531, 1543, 1861, 2281, 2543, 2903, 2953, 3271, 3373, 3673, 3701, 3733, 3793, 3923, 4003, 4241, 4283, 4751, 5333, 5581, 5711, 5801, 5813

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 8*p+3 and 64*p+27 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A005124, A023229. - John Cerkan, Sep 14 2016

Programs

Magma

[n: n in [1..100000] | IsPrime(n) and IsPrime(8*n+3) and IsPrime(64*n+27)] // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime[Range[800]],AllTrue[Rest[NestList[8#+3&,#,2]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 12 2017 *)

Formula

a(n) = 1 or 3 (mod 10) for n > 1. - John Cerkan, Sep 14 2016