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A238447 Primes p such that f(p) and f(f(p)) are both prime, where f(x) = x^2-x-1.

%I A238447 #20 May 22 2025 10:21:37
%S A238447 3,487,617,677,751,1201,1289,1579,1747,2027,2267,2269,2309,3259,3947,
%T A238447 4457,4567,4621,4637,4799,4951,5701,6029,6991,7151,7687,7867,9187,
%U A238447 9209,9341,9587,9829,11321,12301,12541,12781,13177,13649,15919,16349
%N A238447 Primes p such that f(p) and f(f(p)) are both prime, where f(x) = x^2-x-1.
%C A238447 Intersection of A230026 and A091567.
%C A238447 Note that f(f(f(p))) is always composite. - _Zak Seidov_, Nov 10 2014
%H A238447 Zak Seidov, <a href="/A238447/b238447.txt">Table of n, a(n) for n = 1..1000</a>
%e A238447 3 is prime, 3^2-3-1 = 5 is prime, and (3^2-3-1)^2-(3^2-3-1)-1 = 19 is prime. Thus, 3 is a member of this sequence.
%t A238447 Select[Prime[Range[2000]],AllTrue[Rest[NestList[#^2-#-1&,#,2]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Oct 03 2017 *)
%o A238447 (Python)
%o A238447 import sympy
%o A238447 from sympy import isprime
%o A238447 def f(x):
%o A238447   return x**2-x-1
%o A238447 {print(p) for p in range(10**5) if isprime(p) and isprime(f(p)) and isprime(f(f(p)))}
%Y A238447 Cf. A237642, A230026, A091567.
%K A238447 nonn
%O A238447 1,1
%A A238447 _Derek Orr_, Feb 26 2014