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

Offset: 1

Author

J. M. Bergot and Robert Israel, Dec 22 2020

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A081115.

Programs

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)]);

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