A237445 - OEIS

A237445

Primes p such that f(f(p)) is prime, where f(x) = x^4 + x^3 + x^2 + x + 1 = A053699(x).

%I #11 Feb 10 2014 04:26:30

%S 1451,2351,2381,2791,5531,5981,7841,8821,10091,10501,11411,11701,

%T 12011,13241,15271,15331,16691,17231,18341,18671,19891,20981,21911,

%U 23071,23131,23561,23741,24061,25321,27361,29221,30851,30941,31271,32141,33931

%N Primes p such that f(f(p)) is prime, where f(x) = x^4 + x^3 + x^2 + x + 1 = A053699(x).

%C All numbers are congruent to 1 mod 10.

%e 1451 is prime and f(f(1451)) = 387147304469214558406348338836395337085545589397781 is prime. Thus, 1451 is a member of this sequence.

%o (Python)

%o import sympy

%o from sympy import isprime

%o {print(n) for n in range(10**5) if isprime(n) and isprime((n**4+n**3+n**2+n+1)**4+(n**4+n**3+n**2+n+1)**3+(n**4+n**3+n**2+n+1)**2+(n**4+n**3+n**2+n+1)+1)}

%o (PARI) f(x)=x^4+x^3+x^2+x+1;forprime(p=1,35000,ispseudoprime(f(f(p)))&&print1(p",")) \\ _M. F. Hasler_, Feb 09 2014

%Y Cf. A088548, A237361.

%K nonn

%O 1,1

%A _Derek Orr_, Feb 08 2014