|
%I #12 Apr 12 2019 08:25:34
%S 109,149,269,389,409,449,569,829,929,1069,1129,1429,1489,1609,1889,
%T 1949,2129,2269,2309,2549,2609,2689,2749,2789,2909,2969,3109,3209,
%U 3229,3449,3709,3769,3889,4129,4349,4409,4889,4909,4969,5189,5309,5449,5569,5749,6029
%N Prime numbers congruent to 9 modulo 20 representable by x^2 + 100*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. A325073 corresponds to those representable by the first form, and this sequence 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="/A325074/a325074.gp.txt">PARI program for A325074</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 4409:
%e - 4409 is a prime number,
%e - 4409 = 220*20 + 9,
%e - 4409 = 53^2 + 100*4^2,
%e - hence 4409 belongs to this sequence.
%o (PARI) See Links section.
%Y See A325067 for similar results.
%Y Cf. A141883, A325073.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Mar 27 2019
|
