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 A325084 Prime numbers congruent to 1, 65 or 81 modulo 112 neither representable by x^2 + 14*y^2 nor by x^2 + 448*y^2. 3
 113, 193, 337, 401, 641, 1009, 1201, 1297, 2689, 2801, 3089, 3137, 3217, 3329, 3361, 3761, 3889, 4337, 4481, 5009, 5153, 5233, 5441, 5569, 6113, 6337, 6353, 6449, 6577, 6673, 7681, 7841, 8513, 8737, 8929, 9041, 9137, 9521, 9601, 9697, 10369, 10529, 10753 (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. A325083 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 A325084 Wikipedia, Kaplansky's theorem on quadratic forms EXAMPLE Regarding 113: - 113 is a prime number, - 113 = 1*112 + 1, - 113 is neither representable by x^2 + 14*y^2 nor by x^2 + 448*y^2, - hence 113 belongs to this sequence. PROG (PARI) See Links section. CROSSREFS See A325067 for similar results. Cf. A325083. Sequence in context: A142303 A152929 A142180 * A084951 A151947 A087703 Adjacent sequences:  A325081 A325082 A325083 * A325085 A325086 A325087 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 28 2019 STATUS approved

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Last modified May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)