A238447 - OEIS

%I #18 Oct 03 2017 16:32:39

%S 3,487,617,677,751,1201,1289,1579,1747,2027,2267,2269,2309,3259,3947,

%T 4457,4567,4621,4637,4799,4951,5701,6029,6991,7151,7687,7867,9187,

%U 9209,9341,9587,9829,11321,12301,12541,12781,13177,13649,15919,16349

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

%C Intersection of A230026 and A091567.

%C Note that f(f(f(p))) is always composite. - _Zak Seidov_, Nov 10 2014

%H Zak Seidov, <a href="/A238447/b238447.txt">Table of n, a(n) for n = 1..1000</a>

%e 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 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 (Python)

%o import sympy

%o from sympy import isprime

%o def f(x):

%o ..return x**2-x-1

%o {print(p) for p in range(10**5) if isprime(p) and isprime(f(p)) and isprime(f(f(p)))}

%Y Cf. A237642, A230026, A091567.

%K nonn

%O 1,1

%A _Derek Orr_, Feb 26 2014