cp's OEIS Frontend

A237641 Primes p of the form n^2-n-1 (for prime n) such that p^2-p-1 is also prime.

%I A237641 #11 May 22 2025 10:21:36
%S A237641 5,236681,380071,457651,563249,1441199,1660231,2491661,3050261,
%T A237641 4106701,5137021,5146091,5329171,10617821,15574861,19860391,20852921,
%U A237641 21349019,21497131,23025601,24507449,32495699,36342811,48867089,51129649,59082281
%N A237641 Primes p of the form n^2-n-1 (for prime n) such that p^2-p-1 is also prime.
%C A237641 Except a(1), all numbers are congruent to 1 mod 10 or 9 mod 10.
%C A237641 These are the primes in the sequence A237527.
%e A237641 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.
%t A237641 Select[Table[n^2-n-1,{n,Prime[Range[1000]]}],AllTrue[{#,#^2-#-1},PrimeQ]&] (* _Harvey P. Dale_, Aug 14 2024 *)
%o A237641 (Python)
%o A237641 import sympy
%o A237641 from sympy import isprime
%o A237641 def poly2(x):
%o A237641   if isprime(x):
%o A237641     f = x**2-x-1
%o A237641     if isprime(f**2-f-1):
%o A237641       return True
%o A237641   return False
%o A237641 x = 1
%o A237641 while x < 10**5:
%o A237641   if poly2(x):
%o A237641     if isprime(x**2-x-1):
%o A237641       print(x**2-x-1)
%o A237641   x += 1
%o A237641 (PARI)
%o A237641 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 A237641 Cf. A237527, A091567, A091568.
%K A237641 nonn
%O A237641 1,1
%A A237641 _Derek Orr_, Feb 10 2014