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

%I A338300 #13 Apr 23 2025 00:18:18
%S A338300 19,127,3169,24571,698419,863497,3348577,5684257,6156169,7174987,
%T A338300 7646437,10790137,16293691,18637669,19271071,28210267,30384919,
%U A338300 33156901,36760501,45782227,47533141,58887991,62503981,88210519,92224441,100450747,113559769,129356767,138577237,156233617,159017041
%N A338300 Primes p of the form (q^2+q+1)/3 where q is prime and (p^2+p+1)/3 is prime.
%H A338300 Robert Israel, <a href="/A338300/b338300.txt">Table of n, a(n) for n = 1..10000</a>
%e A338300 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.
%p A338300 A:= select(t -> isprime(t) and isprime((t^2+t+1)/3), [seq(i,i=1..30000,6)]):
%p A338300 B:= map(t -> (t^2+t+1)/3, A):
%p A338300 select(t -> isprime((t^2+t+1)/3), B);
%Y A338300 Intersection of A240971 and A338299.
%K A338300 nonn
%O A338300 1,1
%A A338300 _J. M. Bergot_ and _Robert Israel_, Oct 21 2020