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 A325069 #16 Apr 12 2019 08:24:58 %S A325069 41,137,313,409,457,521,569,761,809,857,953,1129,1321,1657,1993,2137, %T A325069 2153,2297,2377,2521,2617,2633,2713,2729,2777,2953,3001,3209,3433, %U A325069 3593,3769,3881,3929,4073,4441,4649,4729,4793,4889,4969,5273,5417,5449,5641,5657 %N A325069 Prime numbers congruent to 9 modulo 16 representable by x^2 + 32*y^2. %C A325069 Kaplansky showed that prime numbers congruent to 9 modulo 16 are representable by exactly one of the quadratic forms x^2 + 32*y^2 or x^2 + 64*y^2. This sequence corresponds to those representable by the first form and A325070 to those representable by the second form. %H A325069 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 A325069 Rémy Sigrist, <a href="/A325069/a325069.gp.txt">PARI program for A325069</a> %H A325069 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a> %e A325069 Regarding 41: %e A325069 - 41 is a prime number, %e A325069 - 41 = 2*16 + 9, %e A325069 - 41 = 3^2 + 32*1^2, %e A325069 - hence 41 belongs to this sequence. %o A325069 (PARI) See Links section. %Y A325069 See A325067 for similar results. %Y A325069 Cf. A105126. %K A325069 nonn %O A325069 1,1 %A A325069 _Rémy Sigrist_, Mar 27 2019