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

1,1

Comments

Subsequence of A002496.

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

Links

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

Example

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.

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

Prog

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

Crossrefs

Cf. A000040, A002496, A177017.

Sequence in context: A218039 A218157 A158370 * A261889 A031726 A154514

Adjacent sequences: A244092 A244093 A244094 * A244096 A244097 A244098

Keyword

nonn

Author

K. D. Bajpai, Jun 20 2014

Status

approved