A023286 Primes that remain prime through 3 iterations of function f(x) = 5x + 8.

7, 13, 43, 223, 757, 883, 2143, 2269, 2521, 2917, 3253, 3967, 4297, 4423, 6229, 6427, 6679, 7621, 7741, 10429, 11353, 12739, 14593, 14929, 15259, 15541, 15937, 16981, 17449, 17911, 21187, 23899, 24697, 25633, 27481, 28789, 29611, 29833, 30253, 30703

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 5*p+8, 25*p+48 and 125*p+248 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023220, A023255, and A111225.

Programs

Magma

[n: n in [1..150000] | IsPrime(n) and IsPrime(5*n+8) and IsPrime(25*n+48) and IsPrime(125*n+248)] // Vincenzo Librandi, Aug 04 2010

Mathematica

it3Q[n_]:=AllTrue[Rest[NestList[5#+8&,n,3]],PrimeQ]; Select[ Prime[ Range[ 3500]],it3Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 21 2015 *)

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 21 2016