A236068 Primes p such that f(f(p)) is prime, where f(x) = x^2 + 1.

3, 5, 13, 43, 47, 127, 263, 277, 293, 337, 347, 397, 443, 467, 487, 503, 577, 593, 607, 673, 727, 733, 773, 857, 887, 907, 1153, 1427, 1487, 1567, 1583, 1637, 1777, 2003, 2213, 2243, 2477, 2503, 2557, 2633, 2687, 2777

Offset: 1

Author

Michel Marcus and Derek Orr, Jan 19 2014

Keywords

• nonn

Examples

			47 is prime and (47^2+1)^2+1 is also prime. So, 47 is a member of this sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A235053.

Programs

Mathematica

Select[Prime[Range[500]],PrimeQ[(#^2+1)^2+1]&] (* Harvey P. Dale, Dec 20 2021 *)

PARI

isok(p) = isprime(p) && (q = p^2+1) && isprime(q^2+1); \\ Michel Marcus, Jan 19 2014

Python

import sympy
from sympy import isprime
{print(p) for p in range(10**4) if isprime(p) and isprime((p**2+1)**2+1)}

Formula

a(n) = (A235053(n)-1)^(1/2).