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%I #15 Apr 12 2019 08:25:42
%S 139,157,367,523,547,607,991,997,1153,1171,1231,1249,1381,1459,1483,
%T 1693,1933,1951,2011,2029,2473,2557,3121,3181,3253,3259,3433,3511,
%U 3643,3877,4111,4447,4603,4663,4759,5521,5749,5827,6007,6163,6217,6301,6397,6451,6553
%N Prime numbers congruent to 1, 16 or 22 modulo 39 representable by both x^2 + x*y + 10*y^2 and 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. This sequence corresponds to those representable by both, and A325076 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="/A325075/a325075.gp.txt">PARI program for A325075</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 997:
%e - 997 is a prime number,
%e - 997 = 25*39 + 22,
%e - 997 = 27^2 + 27*4 + 10*4^2 = 29^2 + 29*1 + 127*1^2,
%e - hence 997 belongs to this sequence.
%o (PARI) See Links section.
%Y See A325067 for similar results.
%Y Cf. A325076.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Mar 28 2019
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