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A244095 Primes of the form (p + q)^2 + 1, where p and q are consecutive primes.

%I A244095 #9 Sep 08 2022 08:46:08
%S A244095 577,1297,7057,8101,14401,41617,44101,57601,90001,115601,147457,
%T A244095 156817,331777,484417,547601,746497,820837,864901,894917,933157,
%U A244095 1299601,1664101,1742401,1822501,1887877,1988101,2131601,2232037,2702737,2944657,3218437
%N A244095 Primes of the form (p + q)^2 + 1, where p and q are consecutive primes.
%C A244095 Subsequence of A002496.
%C A244095 Also, primes of form p^2 + 2pq + q^2 + 1; p and q are consecutive primes.
%H A244095 K. D. Bajpai, <a href="/A244095/b244095.txt">Table of n, a(n) for n = 1..10000</a>
%e A244095 577 is in the sequence because (11 + 13)^2 + 1 = 577, which is prime.
%e A244095 1297 is in the sequence because (17 + 19)^2 + 1 = 1297, which is prime.
%p A244095 with(numtheory):A244095:= proc() local k,p,q; p:=ithprime(n); q:=ithprime(n+1); k:=(p+q)^2 + 1; if isprime(k) then RETURN (k); fi; end: seq(A244095 (), n=1..300);
%t A244095 A244095 = {}; Do[k = (Prime[n] + Prime[n + 1])^2 + 1; If[PrimeQ[k], AppendTo[A244095, k]], {n, 2, 300}]; A244095
%o A244095 (Magma) [t: p in PrimesUpTo(1000) | IsPrime(t) where t is (p+NextPrime(p))^2+1]; // _Bruno Berselli_, Jun 24 2014
%Y A244095 Cf. A000040, A002496, A177017.
%K A244095 nonn
%O A244095 1,1
%A A244095 _K. D. Bajpai_, Jun 20 2014