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.
%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