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

3, 487, 617, 677, 751, 1201, 1289, 1579, 1747, 2027, 2267, 2269, 2309, 3259, 3947, 4457, 4567, 4621, 4637, 4799, 4951, 5701, 6029, 6991, 7151, 7687, 7867, 9187, 9209, 9341, 9587, 9829, 11321, 12301, 12541, 12781, 13177, 13649, 15919, 16349

Offset: 1

Author

Derek Orr, Feb 26 2014

Keywords

• nonn

Comments

Intersection of A230026 and A091567.

Note that f(f(f(p))) is always composite. - Zak Seidov, Nov 10 2014

Examples

			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.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A237642, A230026, A091567.

Programs

Mathematica

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 *)

Python

import sympy
from sympy import isprime
def f(x):
  return x**2-x-1
{print(p) for p in range(10**5) if isprime(p) and isprime(f(p)) and isprime(f(f(p)))}