A339527 - OEIS

A339527

Primes p for which p + k and p^2 + k are prime, where k = (p^2-1)/12.

7, 17, 37, 43, 79, 97, 199, 241, 307, 331, 503, 727, 811, 829, 1297, 1303, 1423, 1879, 2017, 2179, 2593, 2617, 2663, 2953, 3121, 3229, 3761, 3779, 4327, 4357, 4391, 4409, 4663, 4861, 4951, 5021, 5147, 5167, 5237, 5669, 5939, 6569, 7129, 7829, 8269, 8731, 9649, 9781, 10159, 10459, 10531, 10663, 11789

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OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(4) = 43 is a term because with k = (43^2-1)/12 = 154, 43, 43+154 = 197 and 43^2+154 = 2003 are all primes.

MAPLE

select(t -> isprime(t) and isprime((13*t^2-1)/12) and isprime(t+(t^2-1)/12), [seq(seq(12*i+j, j=[1, 5, 7, 11]), i=0..10000)]);

PROG

(PARI) isok(p) = isprime(p) && iferr(isprime(p+(p^2-1)/12) && isprime(p^2+(p^2-1)/12), E, 0); \\ Michel Marcus, Dec 23 2020

CROSSREFS