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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A088483, A088485.

Sequence in context: A041817 A365141 A332259 * A088797 A165589 A184316

Adjacent sequences: A120361 A120362 A120363 * A120365 A120366 A120367

Keyword

nonn

Author

Pierre CAMI, Jun 26 2006

Extensions

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

Status

approved