cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A325075 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.

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%I A325075 #15 Apr 12 2019 08:25:42
%S A325075 139,157,367,523,547,607,991,997,1153,1171,1231,1249,1381,1459,1483,
%T A325075 1693,1933,1951,2011,2029,2473,2557,3121,3181,3253,3259,3433,3511,
%U A325075 3643,3877,4111,4447,4603,4663,4759,5521,5749,5827,6007,6163,6217,6301,6397,6451,6553
%N A325075 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 A325075 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 A325075 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 A325075 Rémy Sigrist, <a href="/A325075/a325075.gp.txt">PARI program for A325075</a>
%H A325075 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e A325075 Regarding 997:
%e A325075 - 997 is a prime number,
%e A325075 - 997 = 25*39 + 22,
%e A325075 - 997 = 27^2 + 27*4 + 10*4^2 = 29^2 + 29*1 + 127*1^2,
%e A325075 - hence 997 belongs to this sequence.
%o A325075 (PARI) See Links section.
%Y A325075 See A325067 for similar results.
%Y A325075 Cf. A325076.
%K A325075 nonn
%O A325075 1,1
%A A325075 _Rémy Sigrist_, Mar 28 2019