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.

A325076 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.

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%I A325076 #14 Apr 12 2019 08:26:03
%S A325076 61,79,211,313,373,601,757,859,919,937,1069,1093,1303,1327,1543,1621,
%T A325076 1699,1777,1873,2083,2089,2161,2239,2341,2551,2707,2713,2731,2791,
%U A325076 2887,3019,3331,3571,3727,3823,4057,4273,4423,4507,4657,4813,4969,4993,5209,5227
%N A325076 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 A325076 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 A325076 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 A325076 Rémy Sigrist, <a href="/A325076/a325076.gp.txt">PARI program for A325076</a>
%H A325076 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e A325076 Regarding 61:
%e A325076 - 61 is a prime number,
%e A325076 - 61 = 39 + 22,
%e A325076 - 61 is neither representable by x^2 + x*y + 10*y^2 nor by x^2 + x*y + 127*y^2,
%e A325076 - hence 61 belongs to this sequence.
%o A325076 (PARI) See Links section.
%Y A325076 See A325067 for similar results.
%Y A325076 Cf. A325075.
%K A325076 nonn
%O A325076 1,1
%A A325076 _Rémy Sigrist_, Mar 28 2019