A338300 Primes p of the form (q^2+q+1)/3 where q is prime and (p^2+p+1)/3 is prime.

19, 127, 3169, 24571, 698419, 863497, 3348577, 5684257, 6156169, 7174987, 7646437, 10790137, 16293691, 18637669, 19271071, 28210267, 30384919, 33156901, 36760501, 45782227, 47533141, 58887991, 62503981, 88210519, 92224441, 100450747, 113559769, 129356767, 138577237, 156233617, 159017041

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 21 2020

Keywords

• nonn

Examples

			a(3) = 3169 is a term because 3169 = (97^2+97+1)/3 and (3169^2+3169+1)/3 = 3348577, and 97, 3169 and 3348577 are all prime.
		

Links

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

Crossrefs

Intersection of A240971 and A338299.

Programs

Maple

A:= select(t -> isprime(t) and isprime((t^2+t+1)/3), [seq(i,i=1..30000,6)]):
B:= map(t -> (t^2+t+1)/3, A):
select(t -> isprime((t^2+t+1)/3), B);