A237527 Numbers n of the form p^2-p-1 = A165900(p), for prime p, such that n^2-n-1 = A165900(n) is also prime.

5, 155, 505, 2755, 3421, 6805, 11341, 27721, 29755, 31861, 44309, 49505, 52211, 65791, 100171, 121451, 134321, 185329, 195805, 236681, 252505, 258571, 292139, 325469, 375155, 380071, 452255, 457651, 465805, 563249, 676505, 1041419, 1061929

Offset: 1

Author

Derek Orr, Feb 09 2014

Keywords

• nonn

Comments

All numbers are congruent to 1 mod 10, 5 mod 10, or 9 mod 10.

A subsequence of A165900 and A028387. - M. F. Hasler, Mar 01 2014

Examples

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

Crossrefs

Cf. A237360, A039914, A002327.

Programs

PARI

s=[]; forprime(p=2, 40000, n=p^2-p-1; if(isprime(n^2-n-1), s=concat(s, n))); s \\ Colin Barker, Feb 10 2014

Python

import sympy
from sympy import isprime
{print(n**2-n-1) for n in range(10**4) if isprime(n) and isprime((n**2-n-1)**2-(n**2-n-1)-1)}

Formula

a(n) = A165900(A230026(n)). - M. F. Hasler, Mar 01 2014