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.

A325083 Prime numbers congruent to 1, 65 or 81 modulo 112 representable by both x^2 + 14*y^2 and x^2 + 448*y^2.

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%I A325083 #15 Apr 12 2019 18:54:03
%S A325083 449,673,977,1409,1873,2017,2081,2129,2417,2657,2753,3313,3697,4001,
%T A325083 4561,4657,4673,4817,4993,6689,6833,7057,7121,7393,7457,7793,8017,
%U A325083 8353,8369,8689,8849,9377,9473,9857,10193,10273,11057,11393,11489,11953,12161,12289
%N A325083 Prime numbers congruent to 1, 65 or 81 modulo 112 representable by both x^2 + 14*y^2 and x^2 + 448*y^2.
%C A325083 Brink showed that prime numbers congruent to 1, 65 or 81 modulo 112 are representable by both or neither of the quadratic forms x^2 + 14*y^2 and x^2 + 448*y^2. This sequence corresponds to those representable by both, and A325084 corresponds to those representable by neither.
%H A325083 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 A325083 Rémy Sigrist, <a href="/A325083/a325083.gp.txt">PARI program for A325083</a>
%H A325083 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e A325083 Regarding 3313:
%e A325083 - 3313 is a prime number,
%e A325083 - 3313 = 29*112 + 65,
%e A325083 - 3313 = 53^2 + 14*6^2 = 39^2 + 448*2^2,
%e A325083 - hence 3313 belongs to this sequence.
%o A325083 (PARI) See Links section.
%Y A325083 See A325067 for similar results.
%Y A325083 Cf. A325084.
%K A325083 nonn
%O A325083 1,1
%A A325083 _Rémy Sigrist_, Mar 28 2019