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