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%I #13 Apr 12 2019 18:53:55
%S 89,179,419,449,599,619,709,719,829,859,1039,1109,1259,1489,1549,1709,
%T 1879,2039,2099,2179,2539,2579,2689,2909,3169,3259,3359,3389,3499,
%U 3919,4019,4159,4229,4349,4409,4799,4909,5009,5039,5179,5449,5569,5659,5779,5839
%N Prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 representable by x^2 + x*y + 69*y^2.
%C Brink showed that prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 are representable by exactly one of the quadratic forms x^2 + x*y + 14*y^2 or x^2 + x*y + 69*y^2. A325081 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="/A325082/a325082.gp.txt">PARI program for A325082</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 2099:
%e - 2099 is a prime number,
%e - 2099 = 38*55 + 9,
%e - 2099 = 17^2 + 1*17*5 + 69*5^2,
%e - hence 2099 belongs to this sequence.
%o (PARI) See Links section.
%Y See A325067 for similar results.
%Y Cf. A325081.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Mar 28 2019
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