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Primes p such that f(f(p)) is prime where f(x) = Phi_6(x).
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%I #7 Feb 10 2014 04:27:03

%S 29,197,673,2297,3613,5923,6133,6917,8219,13553,15667,17137,21911,

%T 30941,33587,35407,38053,44017,45557,46663,51241,53453,65731,67187,

%U 82349,94151,115361,132287,143711,164011,164291,165523,178613,180797,182141

%N Primes p such that f(f(p)) is prime where f(x) = Phi_6(x).

%C Phi_k(x) is the k-th cyclotomic polynomial, see A013595 or A013596.

%e 29 is prime and f(29^6+29^5+29^4+29^3+29^2+29+1) = 54672347801779330810964871392077416495507203132755717 is prime. Thus, 29 is a member of this sequence.

%o (Python)

%o import sympy

%o from sympy import isprime

%o {print(n) for n in range(10**6) if isprime(n) and isprime((n**6+n**5+n**4+n**3+n**2+n+1)**6+(n**6+n**5+n**4+n**3+n**2+n+1)**5+(n**6+n**5+n**4+n**3+n**2+n+1)**4+(n**6+n**5+n**4+n**3+n**2+n+1)**3+(n**6+n**5+n**4+n**3+n**2+n+1)**2+(n**6+n**5+n**4+n**3+n**2+n+1)+1)}

%Y Cf. A088550, A237364.

%K nonn

%O 1,1

%A _Derek Orr_, Feb 08 2014