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 A325078 Prime numbers congruent to 4, 10 or 25 modulo 39 representable by x^2 + x*y + 127*y^2. 3
 127, 199, 283, 337, 433, 571, 727, 829, 883, 907, 1213, 1291, 1297, 1447, 1531, 1609, 1663, 1741, 2053, 2383, 2389, 2677, 3169, 3301, 3319, 3631, 3691, 3709, 3769, 3793, 4003, 4099, 4159, 4549, 4567, 4651, 4729, 4801, 4957, 5347, 5407, 5431, 5563, 5821, 6133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Brink showed that prime numbers congruent to 4, 10 or 25 modulo 39 are representable by exactly one of the quadratic forms x^2 + x*y + 10*y^2 or x^2 + x*y + 127*y^2. A325077 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 A325078 Wikipedia, Kaplansky's theorem on quadratic forms EXAMPLE Regarding 127: - 127 is a prime number, - 127 = 3*39 + 10, - 127 = 0^2 + 0*1 + 127*1^2, - hence 127 belongs to this sequence. PROG (PARI) See Links section. CROSSREFS See A325067 for similar results. Cf. A325077. Sequence in context: A195377 A142090 A095730 * A276261 A343319 A045117 Adjacent sequences:  A325075 A325076 A325077 * A325079 A325080 A325081 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 28 2019 STATUS approved

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Last modified November 28 06:42 EST 2021. Contains 349401 sequences. (Running on oeis4.)