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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
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.
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 A373524
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 28 2019
STATUS
approved