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 A325080 Prime numbers congruent to 1, 16, 26, 31 or 36 modulo 55 neither representable by x^2 + x*y + 14*y^2 nor by x^2 + x*y + 69*y^2. 3
 31, 181, 191, 331, 401, 421, 521, 641, 911, 971, 991, 1021, 1291, 1301, 1511, 1621, 1831, 1871, 2011, 2161, 2281, 2311, 2381, 2861, 3001, 3041, 3061, 3221, 3301, 3331, 3391, 3821, 3931, 4051, 4211, 4261, 4271, 4621, 4691, 4801, 4871, 4931, 4951, 5021, 5171 (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. A325079 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 A325080 Wikipedia, Kaplansky's theorem on quadratic forms EXAMPLE Regarding 31: - 31 is a prime number, - 31 = 0*55 + 31, - 31 is neither representable by x^2 + x*y + 14*y^2 nor by x^2 + x*y + 69*y^2, - hence 31 belongs to this sequence. PROG (PARI) See Links section. CROSSREFS See A325067 for similar results. Cf. A325079. Sequence in context: A140587 A142140 A331759 * A139496 A145838 A243522 Adjacent sequences:  A325077 A325078 A325079 * A325081 A325082 A325083 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.)