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

577, 1297, 7057, 8101, 14401, 41617, 44101, 57601, 90001, 115601, 147457, 156817, 331777, 484417, 547601, 746497, 820837, 864901, 894917, 933157, 1299601, 1664101, 1742401, 1822501, 1887877, 1988101, 2131601, 2232037, 2702737, 2944657, 3218437

Offset: 1

Author

K. D. Bajpai, Jun 20 2014

Keywords

• nonn

Comments

Subsequence of A002496.

Also, primes of form p^2 + 2pq + q^2 + 1; p and q are consecutive primes.

Examples

			577 is in the sequence because (11 + 13)^2 + 1 = 577, which is prime.
1297 is in the sequence because (17 + 19)^2 + 1 = 1297, which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A002496, A177017.

Programs

Magma

[t: p in PrimesUpTo(1000) | IsPrime(t) where t is (p+NextPrime(p))^2+1]; // Bruno Berselli, Jun 24 2014

Maple

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);

Mathematica

A244095 = {}; Do[k = (Prime[n] + Prime[n + 1])^2 + 1; If[PrimeQ[k], AppendTo[A244095, k]], {n, 2, 300}]; A244095