A076727 Primes of the form x^2 + (x+3)^2.

17, 29, 89, 149, 269, 317, 617, 929, 1109, 1409, 2969, 3449, 3617, 4517, 5309, 6389, 7817, 8069, 8849, 12329, 14969, 17117, 17489, 21017, 23117, 23549, 27617, 30509, 32009, 33029, 34589, 35117, 41189, 42929, 43517, 47129, 48989, 52817, 60209

Offset: 1

Author

Cino Hilliard, Oct 28 2002

Keywords

• easy
• nonn

Comments

Each prime of the form 4k+1 has a unique representation as x^2+y^2; these primes have y-x=3.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002144, A027862.

Programs

Magma

[a: n in [0..200] | IsPrime(a) where a is 2*n^2+6*n+9]; // Vincenzo Librandi, Jul 15 2012

Mathematica

Select[Table[2*n^2+6*n+9,{n,0,300}],PrimeQ] (* Vincenzo Librandi, Jul 15 2012 *)

Extensions

Edited by Don Reble, May 03 2006