A237642 Primes of the form n^2-n-1 (for some n) such that p^2-p-1 is also prime.

5, 11, 29, 71, 131, 181, 379, 419, 599, 1979, 2069, 3191, 4159, 13339, 14519, 17291, 19739, 20879, 21169, 26731, 30449, 31151, 39799, 48619, 69959, 70489, 112559, 122849, 132859, 139501, 149381, 183611, 186191, 198469, 212981, 222311, 236681

Offset

1,1

Comments

Except a(1), all numbers are congruent to 1 mod 10 or 9 mod 10.

Links

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

Example

11 is prime and equals 4^2-4-1, and 11^2-11-1 = 109 is prime. So, 11 is a member of this sequence.

Mathematica

Select[Table[n^2-n-1, {n, 500}], AllTrue[{#, #^2-#-1}, PrimeQ]&] (* Harvey P. Dale, Feb 27 2023 *)

Prog

(Python)
import sympy
from sympy import isprime
{print(n**2-n-1) for n in range(10**3) if isprime(n**2-n-1) and isprime((n**2-n-1)**2-(n**2-n-1)-1)}
(PARI)
s=[]; for(n=1, 1000, p=n^2-n-1; if(isprime(p) && isprime(p^2-p-1), s=concat(s, p))); s \\ Colin Barker, Feb 11 2014

Crossrefs

Cf. A002327, A091568.

Sequence in context: A129780 A154504 A106060 * A059508 A084817 A183382

Adjacent sequences: A237639 A237640 A237641 * A237643 A237644 A237645

Keyword

nonn

Author

Derek Orr, Feb 10 2014

Status

approved