A237445 Primes p such that f(f(p)) is prime, where f(x) = x^4 + x^3 + x^2 + x + 1 = A053699(x).

1451, 2351, 2381, 2791, 5531, 5981, 7841, 8821, 10091, 10501, 11411, 11701, 12011, 13241, 15271, 15331, 16691, 17231, 18341, 18671, 19891, 20981, 21911, 23071, 23131, 23561, 23741, 24061, 25321, 27361, 29221, 30851, 30941, 31271, 32141, 33931

Offset

1,1

Comments

All numbers are congruent to 1 mod 10.

Links

Table of n, a(n) for n=1..36.

Example

1451 is prime and f(f(1451)) = 387147304469214558406348338836395337085545589397781 is prime. Thus, 1451 is a member of this sequence.

Prog

(Python)
import sympy
from sympy import isprime
{print(n) for n in range(10**5) if isprime(n) and isprime((n**4+n**3+n**2+n+1)**4+(n**4+n**3+n**2+n+1)**3+(n**4+n**3+n**2+n+1)**2+(n**4+n**3+n**2+n+1)+1)}
(PARI) f(x)=x^4+x^3+x^2+x+1; forprime(p=1, 35000, ispseudoprime(f(f(p)))&&print1(p", ")) \\ M. F. Hasler, Feb 09 2014

Crossrefs

Cf. A088548, A237361.

Sequence in context: A242038 A045099 A325883 * A122421 A187992 A151722

Adjacent sequences: A237442 A237443 A237444 * A237446 A237447 A237448

Keyword

nonn

Author

Derek Orr, Feb 08 2014

Status

approved