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.

A325082 Prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 representable by x^2 + x*y + 69*y^2.

This page as a plain text file.
%I A325082 #13 Apr 12 2019 18:53:55
%S A325082 89,179,419,449,599,619,709,719,829,859,1039,1109,1259,1489,1549,1709,
%T A325082 1879,2039,2099,2179,2539,2579,2689,2909,3169,3259,3359,3389,3499,
%U A325082 3919,4019,4159,4229,4349,4409,4799,4909,5009,5039,5179,5449,5569,5659,5779,5839
%N A325082 Prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 representable by x^2 + x*y + 69*y^2.
%C A325082 Brink showed that prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 are representable by exactly one of the quadratic forms x^2 + x*y + 14*y^2 or x^2 + x*y + 69*y^2. A325081 corresponds to those representable by the first form, and this sequence corresponds to those representable by the second form.
%H A325082 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 A325082 Rémy Sigrist, <a href="/A325082/a325082.gp.txt">PARI program for A325082</a>
%H A325082 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e A325082 Regarding 2099:
%e A325082 - 2099 is a prime number,
%e A325082 - 2099 = 38*55 + 9,
%e A325082 - 2099 = 17^2 + 1*17*5 + 69*5^2,
%e A325082 - hence 2099 belongs to this sequence.
%o A325082 (PARI) See Links section.
%Y A325082 See A325067 for similar results.
%Y A325082 Cf. A325081.
%K A325082 nonn
%O A325082 1,1
%A A325082 _Rémy Sigrist_, Mar 28 2019