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Search: id:A162579
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| A162579 |
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Primes of the form x^2 +y^2 +z^2 +x*y*z, with x, y, and z >0. |
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+0
1
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| 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
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OFFSET
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1,1
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EXAMPLE
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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.
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MATHEMATICA
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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! ]
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CROSSREFS
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Sequence in context: A153422 A166034 A010337 this_sequence A090866 A098062 A094481
Adjacent sequences: A162576 A162577 A162578 this_sequence A162580 A162581 A162582
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 06 2009
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EXTENSIONS
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Definition corrected and entries checked by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 14 2009
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