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