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A339527 Primes p for which p + k and p^2 + k are prime, where k = (p^2-1)/12.

%I A339527 #35 Dec 23 2020 06:17:44
%S A339527 7,17,37,43,79,97,199,241,307,331,503,727,811,829,1297,1303,1423,1879,
%T A339527 2017,2179,2593,2617,2663,2953,3121,3229,3761,3779,4327,4357,4391,
%U A339527 4409,4663,4861,4951,5021,5147,5167,5237,5669,5939,6569,7129,7829,8269,8731,9649,9781,10159,10459,10531,10663,11789
%N A339527 Primes p for which p + k and p^2 + k are prime, where k = (p^2-1)/12.
%H A339527 Robert Israel, <a href="/A339527/b339527.txt">Table of n, a(n) for n = 1..10000</a>
%e A339527 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.
%p A339527 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)]);
%o A339527 (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
%Y A339527 Cf. A081115.
%K A339527 nonn
%O A339527 1,1
%A A339527 _J. M. Bergot_ and _Robert Israel_, Dec 22 2020