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A339917 Primes p such that p+k and p^2+k are prime, where k = (p^2-1)/6.

%I A339917 #10 Dec 23 2020 15:40:22
%S A339917 13,19,71,89,103,139,233,269,409,733,1009,1201,1453,1579,1601,1723,
%T A339917 2053,2143,2251,2699,2753,3181,3259,3271,3361,3491,3739,3923,4051,
%U A339917 4159,4231,4283,4483,4639,4733,5059,5413,5431,5449,6481,6911,7069,7109,7253,7523,7541,7703,7723,7789,7901,8209,9433
%N A339917 Primes p such that p+k and p^2+k are prime, where k = (p^2-1)/6.
%H A339917 Robert Israel, <a href="/A339917/b339917.txt">Table of n, a(n) for n = 1..10000</a>
%e A339917 a(3) = 71 is a term because with k = (71^2-1)/6 = 840, 71, 71+840 = 911 and 71^2+840 = 5881 are all primes.
%p A339917 select(p -> isprime(p) and isprime((7*p^2-1)/6) and isprime((p^2+6*p-1)/6), [seq(seq(6*i+j,j=[1,5]),i=0..10000)]);
%o A339917 (PARI) isok(p) = isprime(p) && iferr(isprime(p+(p^2-1)/6) && isprime(p^2+(p^2-1)/6), E,0); \\ _Michel Marcus_, Dec 23 2020
%Y A339917 Cf. A084922, A339527.
%K A339917 nonn
%O A339917 1,1
%A A339917 _J. M. Bergot_ and _Robert Israel_, Dec 22 2020