A162579 Primes of the form x^2 +y^2 +z^2 +x*y*z, with x, y, and z >0.

13, 29, 53, 89, 109, 113, 137, 149, 157, 173, 193, 197, 229, 257, 269, 277, 293, 313, 317, 337, 349, 353, 373, 389, 409, 433, 449, 461, 509, 557, 593, 613, 617, 653, 673, 677, 701, 709, 733, 757, 769, 773, 797, 809, 829, 853, 877, 929, 941, 953, 977, 997

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Example

13=1^2+2^2+2^2+1*2*2 with x=1, y=z=2. 29=1^2+2^2+4^2+1*2*4 with x=1, y=2, z=4.

Mathematica

f[x_, y_, z_]:=x^2+y^2+z^2+x*y*z; lst={}; Do[Do[Do[p=f[x, y, z]; If[PrimeQ[p], AppendTo[lst, p]], {z, 3*4!}], {y, 3*4!}], {x, 3*4!}]; Take[Union[lst], 5! ]

Crossrefs

Sequence in context: A270361 A010337 A244637 * A286658 A090866 A098062

Adjacent sequences: A162576 A162577 A162578 * A162580 A162581 A162582

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 06 2009

Extensions

Definition corrected and entries checked by R. J. Mathar, Aug 14 2009

Status

approved