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%I #16 Apr 12 2019 08:25:05
%S 73,89,233,281,601,617,937,1033,1049,1097,1193,1289,1433,1481,1609,
%T 1721,1753,1801,1913,2089,2281,2393,2441,2473,2857,2969,3049,3257,
%U 3449,3529,3673,3833,4057,4153,4201,4217,4297,4409,4457,4937,5081,5113,5209,5689,5737
%N Prime numbers congruent to 9 modulo 16 representable by x^2 + 64*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. A325069 corresponds to those representable by the first form and this sequence 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="/A325070/a325070.gp.txt">PARI program for A325070</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 4201:
%e - 4201 is a prime number,
%e - 4201 = 262*16 + 9,
%e - 4201 = 51^2 + 64*5^2,
%e - hence 4201 belongs to this sequence.
%o (PARI) See Links section.
%Y See A325067 for similar results.
%Y Cf. A105126, A325069.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Mar 27 2019