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A325085
Prime numbers congruent to 9, 25 or 57 modulo 112 representable by x^2 + 14*y^2.
3
137, 233, 281, 953, 1033, 1129, 1481, 2137, 2377, 2713, 2857, 2969, 3529, 3593, 3833, 4649, 4729, 5657, 5737, 5849, 6217, 6329, 6521, 6857, 7001, 7561, 8089, 8233, 8297, 8761, 8969, 9209, 9241, 9433, 9689, 10313, 11113, 12377, 12457, 12553, 12601, 12713, 12889
OFFSET
1,1
COMMENTS
Brink showed that prime numbers congruent to 9, 25 or 57 modulo 112 are representable by exactly one of the quadratic forms x^2 + 14*y^2 or x^2 + 448*y^2. This sequence corresponds to those representable by the first form, and A325086 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 11113:
- 11113 is a prime number,
- 11113 = 99*112 + 25,
- 11113 = 103^2 + 14*6^2,
- hence 11113 belongs to this sequence.
PROG
(PARI) See Links section.
CROSSREFS
See A325067 for similar results.
Cf. A325086.
Sequence in context: A142257 A141926 A107164 * A142497 A142523 A307839
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 28 2019
STATUS
approved