A120364 Primes p such that p^2-p-1 and p^2-p+1 are twin primes.

3, 7, 67, 139, 379, 457, 1201, 1381, 1549, 1567, 1747, 1789, 2137, 2557, 2647, 2731, 4057, 4159, 4447, 4561, 5179, 5641, 6397, 9157, 9661, 9829, 9967, 10369, 11467, 11677, 12487, 12781, 13339, 13399, 15241, 17299, 17977, 19207, 19417, 19429

Offset: 1

Author

Pierre CAMI, Jun 26 2006

Keywords

• nonn

Comments

One more than the entries of (A006093 intersect A088485). - Danny Rorabaugh, May 15 2017

Examples

			3*3-3-1=5 3*3-3+1=7, 5 and 7 twin primes so a(1)=3;
5*5-5-1=19 5*5-5+1=21 composite;
7*7-7-1=41 7*7-7+1=43, 41 and 43 twin primes so a(2)=7.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088483, A088485.

Programs

Mathematica

Select[Prime[Range[2500]], PrimeQ[ #^2 - # - 1] && PrimeQ[ #^2 - # + 1] &] (* Stefan Steinerberger, Jul 22 2006 *)
Select[Prime[Range[2500]],AllTrue[#^2-#+{1,-1},PrimeQ]&] (* Harvey P. Dale, Jul 25 2021 *)

Extensions

More terms from Stefan Steinerberger and Rick L. Shepherd, Jul 22 2006