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 A325085 Prime numbers congruent to 9, 25 or 57 modulo 112 representable by x^2 + 14*y^2. 3
 137, 233, 281, 953, 1033, 1129, 1481, 2137, 2377, 2713, 2857, 2969, 3529, 3593, 3833, 4649, 4729, 5657, 5737, 5849, 6217, 6329, 6521, 6857, 7001, 7561, 8089, 8233, 8297, 8761, 8969, 9209, 9241, 9433, 9689, 10313, 11113, 12377, 12457, 12553, 12601, 12713, 12889 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Brink showed that prime numbers congruent to 9, 25 or 57 modulo 112 are representable by exactly one of the quadratic forms x^2 + 14*y^2 or x^2 + 448*y^2. This sequence corresponds to those representable by the first form, and A325086 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 A325085 Wikipedia, Kaplansky's theorem on quadratic forms EXAMPLE Regarding 11113: - 11113 is a prime number, - 11113 = 99*112 + 25, - 11113 = 103^2 + 14*6^2, - hence 11113 belongs to this sequence. PROG (PARI) See Links section. CROSSREFS See A325067 for similar results. Cf. A325086. Sequence in context: A142257 A141926 A107164 * A142497 A142523 A307839 Adjacent sequences:  A325082 A325083 A325084 * A325086 A325087 A325088 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 28 2019 STATUS approved

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Last modified August 10 14:48 EDT 2020. Contains 336381 sequences. (Running on oeis4.)