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
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