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 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