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 A325083 Prime numbers congruent to 1, 65 or 81 modulo 112 representable by both x^2 + 14*y^2 and x^2 + 448*y^2. 3
 449, 673, 977, 1409, 1873, 2017, 2081, 2129, 2417, 2657, 2753, 3313, 3697, 4001, 4561, 4657, 4673, 4817, 4993, 6689, 6833, 7057, 7121, 7393, 7457, 7793, 8017, 8353, 8369, 8689, 8849, 9377, 9473, 9857, 10193, 10273, 11057, 11393, 11489, 11953, 12161, 12289 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Brink showed that prime numbers congruent to 1, 65 or 81 modulo 112 are representable by both or neither of the quadratic forms x^2 + 14*y^2 and x^2 + 448*y^2. This sequence corresponds to those representable by both, and A325084 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 A325083 Wikipedia, Kaplansky's theorem on quadratic forms EXAMPLE Regarding 3313: - 3313 is a prime number, - 3313 = 29*112 + 65, - 3313 = 53^2 + 14*6^2 = 39^2 + 448*2^2, - hence 3313 belongs to this sequence. PROG (PARI) See Links section. CROSSREFS See A325067 for similar results. Cf. A325084. Sequence in context: A319060 A339532 A105376 * A243402 A135073 A160291 Adjacent sequences:  A325080 A325081 A325082 * A325084 A325085 A325086 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 28 2019 STATUS approved

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Last modified November 28 05:30 EST 2021. Contains 349401 sequences. (Running on oeis4.)