login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Primes p such that f(f(p)) is prime where f(x) = x^4 + 1.
0

%I #10 Jan 26 2014 03:22:40

%S 3,79,83,107,211,401,491,881,1013,1061,1367,1637,1669,1811,2029,2309,

%T 2399,2459,2671,2713,2963,3109,3203,3407,3593,3709,3733,3929,4219,

%U 4457,4513,4639,4703,4729,5417,5641,6047,6113

%N Primes p such that f(f(p)) is prime where f(x) = x^4 + 1.

%F a(n) = (A235982(n)-1)^(1/4).

%e 881 is prime and (881^4+1)^4+1 is also prime. So, 881 is a member of this sequence.

%o (Python)

%o import sympy

%o from sympy import isprime

%o {print(p) for p in range(10**4) if isprime(p) and isprime((p**4+1)**4+1)}

%o (PARI) isok(p) = isprime(p) && (q = p^4+1) && isprime(q^4+1); \\ _Michel Marcus_, Jan 19 2014

%Y Cf. A235982.

%K nonn

%O 1,1

%A _Michel Marcus_ and _Derek Orr_, Jan 19 2014