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%I #7 Feb 11 2014 16:50:08
%S 5,236681,380071,457651,563249,1441199,1660231,2491661,3050261,
%T 4106701,5137021,5146091,5329171,10617821,15574861,19860391,20852921,
%U 21349019,21497131,23025601,24507449,32495699,36342811,48867089,51129649,59082281
%N Primes p of the form n^2-n-1 (for prime n) such that p^2-p-1 is also prime.
%C Except a(1), all numbers are congruent to 1 mod 10 or 9 mod 10.
%C These are the primes in the sequence A237527.
%e 5 = 3^2-3^1-1 (3 is prime) and 5^2-5-1 = 19 is prime. Since 5 is prime too, 5 is a member of this sequence.
%o (Python)
%o import sympy
%o from sympy import isprime
%o def poly2(x):
%o ..if isprime(x):
%o ....f = x**2-x-1
%o ....if isprime(f**2-f-1):
%o ......return True
%o ..return False
%o x = 1
%o while x < 10**5:
%o ..if poly2(x):
%o ....if isprime(x**2-x-1):
%o ......print(x**2-x-1)
%o ..x += 1
%o (PARI)
%o s=[]; forprime(n=2, 40000, p=n^2-n-1; if(isprime(p) && isprime(p^2-p-1), s=concat(s, p))); s \\ _Colin Barker_, Feb 11 2014
%Y Cf. A237527, A091567, A091568.
%K nonn
%O 1,1
%A _Derek Orr_, Feb 10 2014
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