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%I #14 Apr 12 2019 08:25:27
%S 29,89,229,349,509,709,769,809,1009,1049,1109,1229,1249,1289,1409,
%T 1549,1669,1709,1789,2029,2069,2089,2389,2729,3049,3089,3169,3329,
%U 3389,3469,3529,3929,3989,4049,4229,4289,4549,4649,4729,4789,5009,5209,5669,5689,5849
%N Prime numbers congruent to 9 modulo 20 representable by x^2 + 20*y^2.
%C Brink showed that prime numbers congruent to 9 modulo 20 are representable by exactly one of the quadratic forms x^2 + 20*y^2 or x^2 + 100*y^2. This sequence corresponds to those representable by the first form, and A325074 corresponds 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="/A325073/a325073.gp.txt">PARI program for A325073</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 1009:
%e - 1009 is a prime number,
%e - 1009 = 50*20 + 9,
%e - 1009 = 17^2 + 20*6^2,
%e - hence 1009 belongs to this sequence.
%o (PARI) See Links section.
%Y See A325067 for similar results.
%Y Cf. A141883, A325074.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Mar 27 2019