A237366 - OEIS

%I #7 Feb 07 2014 10:27:27

%S 7,19,31,67,127,181,223,241,331,367,409,463,487,673,709,751,811,823,

%T 883,997,1117,1231,1321,1489,1549,1861,1933,2083,2179,2287,2473,2551,

%U 2707,2803,2851,2857,2917,2971,3067,3361,3499,3559,3691,3847,3931

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

%e 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.

%o (Python)

%o import sympy

%o from sympy import isprime

%o {print(n) for n in range(10**4) if isprime(n) and isprime((n**2+n+1)**2+(n**2+n+1)+1)}

%o (PARI)

%o 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

%Y Cf. A237360, A002383.

%K nonn

%O 1,1

%A _Derek Orr_, Feb 06 2014