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 A325081 Prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 representable by x^2 + x*y + 14*y^2. 3
 59, 199, 229, 269, 379, 389, 499, 509, 839, 929, 1049, 1279, 1409, 1439, 1499, 1609, 1699, 2029, 2069, 2269, 2399, 2699, 2729, 2819, 3019, 3089, 3469, 3529, 3719, 4049, 4079, 4129, 4139, 4339, 4519, 4679, 4789, 4889, 4999, 5119, 5399, 5479, 5669, 6029, 6229 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Brink showed that prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 are representable by exactly one of the quadratic forms x^2 + x*y + 14*y^2 or x^2 + x*y + 69*y^2. This sequence corresponds to those representable by the first form, and A325082 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 A325081 Wikipedia, Kaplansky's theorem on quadratic forms EXAMPLE Regarding 4999: - 4999 is a prime number, - 4999 = 90*55 + 49, - 4999 = 41^2 + 41*14 + 14*14^2, - hence 4999 belongs to this sequence. PROG (PARI) See Links section. CROSSREFS See A325067 for similar results. Cf. A325082. Sequence in context: A142064 A114353 A210653 * A142092 A142215 A141977 Adjacent sequences:  A325078 A325079 A325080 * A325082 A325083 A325084 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 28 2019 STATUS approved

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Last modified October 14 17:31 EDT 2019. Contains 328022 sequences. (Running on oeis4.)