cp's OEIS Frontend

A230026 Primes p such that f(f(p)) is prime, where f(n) = n^2-n-1 = A165900(n).

%I A230026 #26 Mar 20 2020 10:01:46
%S A230026 3,13,23,53,59,83,107,167,173,179,211,223,229,257,317,349,367,431,443,
%T A230026 487,503,509,541,571,613,617,673,677,683,751,823,1021,1031,1093,1103,
%U A230026 1109,1123,1201,1231,1289,1301,1319,1361,1373,1427,1451
%N A230026 Primes p such that f(f(p)) is prime, where f(n) = n^2-n-1 = A165900(n).
%C A230026 Note that f(f(f(n))) = (-1 + 4*n - 3*n^3 + n^4)*(1 + n - 3*n^2 - n^3 +  n^4) is always composite. - _Zak Seidov_, Nov 10 2014
%F A230026 A237527(n) = A165900(a(n)). - _M. F. Hasler_, Mar 01 2014
%e A230026 3 is prime and (3^2-3-1)^2-(3^2-3-1)-1 = 19 is also prime. So, 3 is a member of this sequence.
%o A230026 (Python)
%o A230026 import sympy
%o A230026 from sympy import isprime
%o A230026 def f(x):
%o A230026     return x**2-x-1
%o A230026 {p for p in range(10**4) if isprime(p) and isprime(f(f(p)))}
%o A230026 (Sage)
%o A230026 f = lambda x: x^2-x-1
%o A230026 [p for p in primes(1452) if is_prime(f(f(p)))] # _Peter Luschny_, Mar 02 2014
%Y A230026 Cf. A000040, A237527, A002327.
%K A230026 nonn
%O A230026 1,1
%A A230026 _Derek Orr_, Feb 23 2014