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%I #13 Apr 12 2019 18:53:40
%S 31,181,191,331,401,421,521,641,911,971,991,1021,1291,1301,1511,1621,
%T 1831,1871,2011,2161,2281,2311,2381,2861,3001,3041,3061,3221,3301,
%U 3331,3391,3821,3931,4051,4211,4261,4271,4621,4691,4801,4871,4931,4951,5021,5171
%N Prime numbers congruent to 1, 16, 26, 31 or 36 modulo 55 neither representable by x^2 + x*y + 14*y^2 nor by x^2 + x*y + 69*y^2.
%C Brink showed that prime numbers congruent to 1, 16, 26, 31 or 36 modulo 55 are representable by both or neither of the quadratic forms x^2 + x*y + 14*y^2 and x^2 + x*y + 69*y^2. A325079 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="/A325080/a325080.gp.txt">PARI program for A325080</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 31:
%e - 31 is a prime number,
%e - 31 = 0*55 + 31,
%e - 31 is neither representable by x^2 + x*y + 14*y^2 nor by x^2 + x*y + 69*y^2,
%e - hence 31 belongs to this sequence.
%o (PARI) See Links section.
%Y See A325067 for similar results.
%Y Cf. A325079.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Mar 28 2019