A237641 Primes p of the form n^2-n-1 (for prime n) such that p^2-p-1 is also prime.

5, 236681, 380071, 457651, 563249, 1441199, 1660231, 2491661, 3050261, 4106701, 5137021, 5146091, 5329171, 10617821, 15574861, 19860391, 20852921, 21349019, 21497131, 23025601, 24507449, 32495699, 36342811, 48867089, 51129649, 59082281

Offset

1,1

Comments

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

These are the primes in the sequence A237527.

Links

Table of n, a(n) for n=1..26.

Example

5 = 3^2-3^1-1 (3 is prime) and 5^2-5-1 = 19 is prime. Since 5 is prime too, 5 is a member of this sequence.

Prog

(Python)
import sympy
from sympy import isprime
def poly2(x):
..if isprime(x):
....f = x**2-x-1
....if isprime(f**2-f-1):
......return True
..return False
x = 1
while x < 10**5:
..if poly2(x):
....if isprime(x**2-x-1):
......print(x**2-x-1)
..x += 1
(PARI)
s=[]; forprime(n=2, 40000, 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. A237527, A091567, A091568.

Sequence in context: A151589 A243114 A038027 * A057679 A123751 A152516

Adjacent sequences: A237638 A237639 A237640 * A237642 A237643 A237644

Keyword

nonn

Author

Derek Orr, Feb 10 2014

Status

approved