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
Keywords
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
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Mathematica
Select[Prime[Range[500]],PrimeQ[(#^2+1)^2+1]&] (* Harvey P. Dale, Dec 20 2021 *)
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PARI
isok(p) = isprime(p) && (q = p^2+1) && isprime(q^2+1); \\ Michel Marcus, Jan 19 2014
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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).