A355982 Primes in A004253.

19, 2089, 10009, 229771, 1100899, 2779769539, 33629651653051, 161129341280179, 3698955932459041, 406851522918841459, 23583148518971728185859, 720404932310119551295422832411, 4593030255749728350335873388896105689, 6111807570415039356543996013033519421475691

Offset: 1

Author

R. J. Mathar, Jul 22 2022

Keywords

• nonn

Comments

Related to the search of solutions of pair of congruences p^2 == -3 (mod q), q^2 == -3 (mod p).

Cosgrave and Dilcher list indices of these primes 2, 5, 6, 8, 9, 14, 20, 21, 23, 26, ... up to 25000 (assuming offset 0 in A004253), including probable primes.

Links

• J. B. Cosgrave and K. Dilcher, Pairs of reciprocal quadratic congruences involving primes, Fib. Quart. 51 (2) (2013) 98, after Theorem 5.

Crossrefs

Cf. A004253.

Programs

Mathematica

Select[LinearRecurrence[{5, -1}, {1, 4}, 200], PrimeQ] (* Paolo Xausa, Mar 19 2024 *)

Formula

A000040 INTERSECT A004253.

Extensions

More terms from Jinyuan Wang, Jul 22 2022