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 A325074 Prime numbers congruent to 9 modulo 20 representable by x^2 + 100*y^2. 3
 109, 149, 269, 389, 409, 449, 569, 829, 929, 1069, 1129, 1429, 1489, 1609, 1889, 1949, 2129, 2269, 2309, 2549, 2609, 2689, 2749, 2789, 2909, 2969, 3109, 3209, 3229, 3449, 3709, 3769, 3889, 4129, 4349, 4409, 4889, 4909, 4969, 5189, 5309, 5449, 5569, 5749, 6029 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893. Rémy Sigrist, PARI program for A325074 Wikipedia, Kaplansky's theorem on quadratic forms EXAMPLE Regarding 4409: - 4409 is a prime number, - 4409 = 220*20 + 9, - 4409 = 53^2 + 100*4^2, - hence 4409 belongs to this sequence. PROG (PARI) See Links section. CROSSREFS See A325067 for similar results. Cf. A141883, A325073. Sequence in context: A095609 A046295 A164288 * A182476 A182451 A161483 Adjacent sequences: A325071 A325072 A325073 * A325075 A325076 A325077 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 27 2019 STATUS approved

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Last modified March 22 17:48 EDT 2023. Contains 361432 sequences. (Running on oeis4.)