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.

A325085 Prime numbers congruent to 9, 25 or 57 modulo 112 representable by x^2 + 14*y^2.

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%I A325085 #12 Apr 12 2019 18:54:30
%S A325085 137,233,281,953,1033,1129,1481,2137,2377,2713,2857,2969,3529,3593,
%T A325085 3833,4649,4729,5657,5737,5849,6217,6329,6521,6857,7001,7561,8089,
%U A325085 8233,8297,8761,8969,9209,9241,9433,9689,10313,11113,12377,12457,12553,12601,12713,12889
%N A325085 Prime numbers congruent to 9, 25 or 57 modulo 112 representable by x^2 + 14*y^2.
%C A325085 Brink showed that prime numbers congruent to 9, 25 or 57 modulo 112 are representable by exactly one of the quadratic forms x^2 + 14*y^2 or x^2 + 448*y^2. This sequence corresponds to those representable by the first form, and A325086 corresponds to those representable by the second form.
%H A325085 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 A325085 Rémy Sigrist, <a href="/A325085/a325085.gp.txt">PARI program for A325085</a>
%H A325085 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e A325085 Regarding 11113:
%e A325085 - 11113 is a prime number,
%e A325085 - 11113 = 99*112 + 25,
%e A325085 - 11113 = 103^2 + 14*6^2,
%e A325085 - hence 11113 belongs to this sequence.
%o A325085 (PARI) See Links section.
%Y A325085 See A325067 for similar results.
%Y A325085 Cf. A325086.
%K A325085 nonn
%O A325085 1,1
%A A325085 _Rémy Sigrist_, Mar 28 2019