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A244095
Primes of the form (p + q)^2 + 1, where p and q are consecutive primes.
1
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
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
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Jun 20 2014
STATUS
approved