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 A325076 Prime numbers congruent to 1, 16 or 22 modulo 39 neither representable by x^2 + x*y + 10*y^2 nor by x^2 + x*y + 127*y^2. 3
 61, 79, 211, 313, 373, 601, 757, 859, 919, 937, 1069, 1093, 1303, 1327, 1543, 1621, 1699, 1777, 1873, 2083, 2089, 2161, 2239, 2341, 2551, 2707, 2713, 2731, 2791, 2887, 3019, 3331, 3571, 3727, 3823, 4057, 4273, 4423, 4507, 4657, 4813, 4969, 4993, 5209, 5227 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Brink showed that prime numbers congruent to 1, 16 or 22 modulo 39 are representable by both or neither of the quadratic forms x^2 + x*y + 10*y^2 and x^2 + x*y + 127*y^2. A325075 corresponds to those representable by both, and this sequence corresponds to those representable by neither. 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 A325076 Wikipedia, Kaplansky's theorem on quadratic forms EXAMPLE Regarding 61: - 61 is a prime number, - 61 = 39 + 22, - 61 is neither representable by x^2 + x*y + 10*y^2 nor by x^2 + x*y + 127*y^2, - hence 61 belongs to this sequence. PROG (PARI) See Links section. CROSSREFS See A325067 for similar results. Cf. A325075. Sequence in context: A217076 A281960 A139931 * A253232 A245759 A186457 Adjacent sequences:  A325073 A325074 A325075 * A325077 A325078 A325079 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 28 2019 STATUS approved

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Last modified January 24 16:47 EST 2020. Contains 331209 sequences. (Running on oeis4.)