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 A325079 Prime numbers congruent to 1, 16, 26, 31 or 36 modulo 55 representable by both x^2 + x*y + 14*y^2 and x^2 + x*y + 69*y^2. 3
 71, 251, 311, 631, 661, 691, 751, 881, 1061, 1171, 1181, 1321, 1571, 1721, 1741, 1901, 1951, 2341, 2531, 2621, 2671, 2711, 2731, 2971, 3191, 3271, 3371, 3491, 3631, 3701, 3851, 3881, 4481, 4591, 4651, 5261, 5471, 5501, 5531, 5581, 5641, 5701, 5861, 6121, 6271 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Brink showed that prime numbers congruent to 1, 16, 26, 31 or 36 modulo 55 are representable by both or neither of the quadratic forms x^2 + x*y + 14*y^2 and x^2 + x*y + 69*y^2. This sequence corresponds to those representable by both, and A325080 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 A325079 Wikipedia, Kaplansky's theorem on quadratic forms EXAMPLE Regarding 881: - 881 is a prime number, - 881 = 16*55 + 1, - 881 = 3^2 + 3*(-8) + 14*(-8)^2 = 28^2 + 28*1 + 69*1^2, - hence 881 belongs to this sequence. PROG (PARI) See Links section. CROSSREFS See A325067 for similar results. Cf. A325080. Sequence in context: A001126 A140628 A123038 * A142325 A232475 A243579 Adjacent sequences:  A325076 A325077 A325078 * A325080 A325081 A325082 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 28 2019 STATUS approved

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Last modified May 7 07:37 EDT 2021. Contains 343636 sequences. (Running on oeis4.)