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Primes in A004253.
0

%I #16 Mar 19 2024 16:16:20

%S 19,2089,10009,229771,1100899,2779769539,33629651653051,

%T 161129341280179,3698955932459041,406851522918841459,

%U 23583148518971728185859,720404932310119551295422832411,4593030255749728350335873388896105689,6111807570415039356543996013033519421475691

%N Primes in A004253.

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

%C 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.

%H J. B. Cosgrave and K. Dilcher, <a href="https://fq.math.ca/Papers1/51-2/CosgraveDilcher-1.pdf">Pairs of reciprocal quadratic congruences involving primes</a>, Fib. Quart. 51 (2) (2013) 98, after Theorem 5.

%F A000040 INTERSECT A004253.

%t Select[LinearRecurrence[{5, -1}, {1, 4}, 200], PrimeQ] (* _Paolo Xausa_, Mar 19 2024 *)

%Y Cf. A004253.

%K nonn

%O 1,1

%A _R. J. Mathar_, Jul 22 2022

%E More terms from _Jinyuan Wang_, Jul 22 2022