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A237364 Numbers n of the form n=Phi(7,p) (for prime p) such that Phi(7,n) is also prime.

%I A237364 #10 Feb 07 2014 05:02:53
%S A237364 616067011,58749951412747,93054242152309543,146945091162352770847,
%T A237364 2224989620406870255043,43184085337135904888293,
%U A237364 53224134341571172990843,109539169818149034933067,308295173856880401026941,6197901576526752380316343,14789135287218506962379317
%N A237364 Numbers n of the form n=Phi(7,p) (for prime p) such that Phi(7,n) is also prime.
%C A237364 Phi(7,x) =1+x+x^2+x^3+x^4+x^5+x^6 =A053716(x) is the 7th cyclotomic polynomial.
%e A237364 616067011 = 29^6+29^5+29^4+29^3+29^2+29+1 (29 is prime) and 616067011^6+616067011^5+616067011^4+616067011^3+616067011^2+616067011+1 = 54672347801779330810964871392077416495507203132755717 is prime. Thus, 616067011 is a member of this sequence.
%p A237364 for k from 1 do
%p A237364     p := ithprime(k) ;
%p A237364     n := numtheory[cyclotomic](7,p) ;
%p A237364     pn := numtheory[cyclotomic](7,n) ;
%p A237364     if isprime( pn) then
%p A237364         print(n) ;
%p A237364     end if;
%p A237364 end do: # _R. J. Mathar_, Feb 07 2014
%o A237364 (Python)
%o A237364 import sympy
%o A237364 from sympy import isprime
%o A237364 {print(n**6+n**5+n**4+n**3+n**2+n+1) for n in range(10**5) 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 A237364 Cf. A088550.
%K A237364 nonn
%O A237364 1,1
%A A237364 _Derek Orr_, Feb 06 2014