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.

A325079 Prime numbers congruent to 1, 16, 26, 31 or 36 modulo 55 representable by both x^2 + x*y + 14*y^2 and x^2 + x*y + 69*y^2.

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%I A325079 #15 Apr 12 2019 18:53:31
%S A325079 71,251,311,631,661,691,751,881,1061,1171,1181,1321,1571,1721,1741,
%T A325079 1901,1951,2341,2531,2621,2671,2711,2731,2971,3191,3271,3371,3491,
%U A325079 3631,3701,3851,3881,4481,4591,4651,5261,5471,5501,5531,5581,5641,5701,5861,6121,6271
%N A325079 Prime numbers congruent to 1, 16, 26, 31 or 36 modulo 55 representable by both x^2 + x*y + 14*y^2 and x^2 + x*y + 69*y^2.
%C A325079 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. This sequence corresponds to those representable by both, and A325080 corresponds to those representable by neither.
%H A325079 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 A325079 Rémy Sigrist, <a href="/A325079/a325079.gp.txt">PARI program for A325079</a>
%H A325079 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e A325079 Regarding 881:
%e A325079 - 881 is a prime number,
%e A325079 - 881 = 16*55 + 1,
%e A325079 - 881 = 3^2 + 3*(-8) + 14*(-8)^2 = 28^2 + 28*1 + 69*1^2,
%e A325079 - hence 881 belongs to this sequence.
%o A325079 (PARI) See Links section.
%Y A325079 See A325067 for similar results.
%Y A325079 Cf. A325080.
%K A325079 nonn
%O A325079 1,1
%A A325079 _Rémy Sigrist_, Mar 28 2019