S000076


Primes not of the form x^2 + y^2 + z^2 + x*y + x*z + y*z for positive x, y, and z.

2, 3, 5, 7, 13, 19, 23, 29, 31, 37, 41, 53, 59, 79, 101, 107, 127, 149, 167, 211, 239, 317, 401, 479, 541, 659, 1031, 1409, 1439, 2459, 2543

1

S000076

This sequence appears to be finite.

T. D. Noe, Plot of 31 terms

(Mma) nn = 200; c = {1, 1, 1, 1, 1, 1}; t = Select[Union[Flatten[Table[c.{x^2, y^2, z^2, x*y, x*z, y*z}, {x, nn}, {y, nn}, {z, nn}]]], # <= nn^2 && PrimeQ[#] &]; Complement[Prime[Range[PrimePi[t[[-1]]]]], t]

Cf. S000075 (complement in the primes).

nonn

T. D. Noe, Jun 09 2014

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