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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..43.

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 A325085

Wikipedia, Kaplansky's theorem on quadratic forms

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

Adjacent sequences:  A325082 A325083 A325084 * A325086 A325087 A325088

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Mar 28 2019

STATUS

approved

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Last modified August 10 14:48 EDT 2020. Contains 336381 sequences. (Running on oeis4.)