cp's OEIS Frontend

A237361 Numbers n of the form n = Phi_5(p) (for prime p) such that Phi_5(n) is also prime.

%I A237361 #27 Feb 17 2014 01:55:48
%S A237361 4435770414505,30562950873505,32152890387805,60700878873905,
%T A237361 936037312559305,1279875801783805,3780430049614405,6055088920612205,
%U A237361 10370026462436905,12160851727605005,16956369914710105,18746881534017005,20813869508536105,30740855019988405
%N A237361 Numbers n of the form n = Phi_5(p) (for prime p) such that Phi_5(n) is also prime.
%C A237361 Phi_5(x) = x^4 + x^3 + x^2 + x + 1 is the fifth cyclotomic polynomial, see A053699.
%C A237361 All numbers are congruent to 5 mod 100.
%C A237361 The definition requires p to be prime, Phi_5(p) does not need to be prime, but Phi_5(Phi_5(p)) must be prime.
%e A237361 4435770414505 = 1451^4+1451^3+1451^2+1451+1 (1451 is prime), and 4435770414505^4+4435770414505^3+4435770414505^2+4435770414505+1 = 387147304469214558406348338836395337085545589397781 is prime. Thus, 4435770414505 is a member of this sequence.
%o A237361 (Python)
%o A237361 import sympy
%o A237361 from sympy import isprime
%o A237361 {print(n**4+n**3+n**2+n+1) 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 A237361 (PARI) forprime(p=2,1e7, k=polcyclo(5,p) ; if( ispseudoprime(polcyclo(5,k)), print1(k", "))) \\ _Charles R Greathouse IV_, Feb 07 2014
%Y A237361 Cf. A131992, A088548.
%K A237361 nonn
%O A237361 1,1
%A A237361 _Derek Orr_, Feb 06 2014