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

%I A236068 #16 Dec 20 2021 14:45:02
%S A236068 3,5,13,43,47,127,263,277,293,337,347,397,443,467,487,503,577,593,607,
%T A236068 673,727,733,773,857,887,907,1153,1427,1487,1567,1583,1637,1777,2003,
%U A236068 2213,2243,2477,2503,2557,2633,2687,2777
%N A236068 Primes p such that f(f(p)) is prime, where f(x) = x^2 + 1.
%H A236068 Harvey P. Dale, <a href="/A236068/b236068.txt">Table of n, a(n) for n = 1..1000</a>
%F A236068 a(n) = (A235053(n)-1)^(1/2).
%e A236068 47 is prime and (47^2+1)^2+1 is also prime. So, 47 is a member of this sequence.
%t A236068 Select[Prime[Range[500]],PrimeQ[(#^2+1)^2+1]&] (* _Harvey P. Dale_, Dec 20 2021 *)
%o A236068 (Python)
%o A236068 import sympy
%o A236068 from sympy import isprime
%o A236068 {print(p) for p in range(10**4) if isprime(p) and isprime((p**2+1)**2+1)}
%o A236068 (PARI) isok(p) = isprime(p) && (q = p^2+1) && isprime(q^2+1); \\ _Michel Marcus_, Jan 19 2014
%Y A236068 Cf. A235053.
%K A236068 nonn
%O A236068 1,1
%A A236068 _Michel Marcus_ and _Derek Orr_, Jan 19 2014