%N Prime numbers congruent to 1, 16 or 22 modulo 39 neither representable by x^2 + x*y + 10*y^2 nor by x^2 + x*y + 127*y^2.
%C Brink showed that prime numbers congruent to 1, 16 or 22 modulo 39 are representable by both or neither of the quadratic forms x^2 + x*y + 10*y^2 and x^2 + x*y + 127*y^2. A325075 corresponds to those representable by both, and this sequence corresponds to those representable by neither.
%H David Brink, <a href="https://doi.org/10.1016/j.jnt.2008.04.007">Five peculiar theorems on simultaneous representation of primes by quadratic forms</a>, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893.
%H Rémy Sigrist, <a href="/A325076/a325076.gp.txt">PARI program for A325076</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e Regarding 61:
%e - 61 is a prime number,
%e - 61 = 39 + 22,
%e - 61 is neither representable by x^2 + x*y + 10*y^2 nor by x^2 + x*y + 127*y^2,
%e - hence 61 belongs to this sequence.
%o (PARI) See Links section.
%Y See A325067 for similar results.
%Y Cf. A325075.
%A _Rémy Sigrist_, Mar 28 2019