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.

A325080 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.

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%I A325080 #13 Apr 12 2019 18:53:40
%S A325080 31,181,191,331,401,421,521,641,911,971,991,1021,1291,1301,1511,1621,
%T A325080 1831,1871,2011,2161,2281,2311,2381,2861,3001,3041,3061,3221,3301,
%U A325080 3331,3391,3821,3931,4051,4211,4261,4271,4621,4691,4801,4871,4931,4951,5021,5171
%N A325080 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 A325080 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 A325080 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 A325080 Rémy Sigrist, <a href="/A325080/a325080.gp.txt">PARI program for A325080</a>
%H A325080 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e A325080 Regarding 31:
%e A325080 - 31 is a prime number,
%e A325080 - 31 = 0*55 + 31,
%e A325080 - 31 is neither representable by x^2 + x*y + 14*y^2 nor by x^2 + x*y + 69*y^2,
%e A325080 - hence 31 belongs to this sequence.
%o A325080 (PARI) See Links section.
%Y A325080 See A325067 for similar results.
%Y A325080 Cf. A325079.
%K A325080 nonn
%O A325080 1,1
%A A325080 _Rémy Sigrist_, Mar 28 2019