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 A325067 #22 Apr 19 2019 13:45:10 %S A325067 113,257,337,353,577,593,881,1153,1201,1217,1249,1553,1601,1777,1889, %T A325067 2113,2129,2273,2593,2657,2689,2833,3089,3121,3137,3217,3313,3361, %U A325067 3761,4001,4049,4177,4273,4289,4481,4513,4657,4721,4801,4817,4993,5233,5297,5393 %N A325067 Prime numbers congruent to 1 modulo 16 representable by both x^2 + 32*y^2 and x^2 + 64*y^2. %C A325067 Kaplansky showed that prime numbers congruent to 1 modulo 16 are representable by both or neither of the quadratic forms x^2 + 32*y^2 and x^2 + 64*y^2. This sequence corresponds to those representable by both, and A325068 corresponds to those representable by neither. %C A325067 Also, Kaplansky showed that prime numbers congruent to 9 modulo 16 are representable by exactly one of these quadratic forms. A325069 corresponds to those representable by the first form and A325070 to those representable by the second form. %C A325067 Brink provided similar results for other congruences. %H A325067 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 A325067 Rémy Sigrist, <a href="/A325067/a325067.gp.txt">PARI program for A325067</a> %H A325067 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a> %e A325067 Regarding 1201: %e A325067 - 1201 is a prime number, %e A325067 - 1201 = 75*16 + 1, %e A325067 - 1201 = 7^2 + 32*6^2 = 25^2 + 64*3^2, %e A325067 - hence 1201 belongs to the sequence. %o A325067 (PARI) See Links section. %Y A325067 Cf. A094407, A105126, A325068, A325069, A325070. %Y A325067 See A325071, A325072, A325073 and A325074 for similar results in congruences modulo 16. %Y A325067 See A325075, A325076, A325077 and A325078 for similar results in congruences modulo 39. %Y A325067 See A325079, A325080, A325081 and A325082 for similar results in congruences modulo 55. %Y A325067 See A325083, A325084, A325085 and A325086 for similar results in congruences modulo 112. %Y A325067 See A325087, A325088, A325089 and A325090 for similar results in congruences modulo 240. %K A325067 nonn %O A325067 1,1 %A A325067 _Rémy Sigrist_, Mar 27 2019