A237366 Primes p such that f(f(p)) is prime where f(x) = x^2+x+1.

7, 19, 31, 67, 127, 181, 223, 241, 331, 367, 409, 463, 487, 673, 709, 751, 811, 823, 883, 997, 1117, 1231, 1321, 1489, 1549, 1861, 1933, 2083, 2179, 2287, 2473, 2551, 2707, 2803, 2851, 2857, 2917, 2971, 3067, 3361, 3499, 3559, 3691, 3847, 3931

Offset: 1

Author

Derek Orr, Feb 06 2014

Keywords

• nonn

Examples

			31 is prime and (31^2+31+1)^2+(31^2+31+1)+1 = 987043 is prime. Thus, 31 is a member of this sequence.
		

Crossrefs

Cf. A237360, A002383.

Programs

PARI

s=[]; forprime(p=2, 4000, if(isprime(p^4+2*p^3+4*p^2+3*p+3), s=concat(s, p))); s \\ Colin Barker, Feb 07 2014

Python

import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(n) and isprime((n**2+n+1)**2+(n**2+n+1)+1)}