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A325086 Prime numbers congruent to 9, 25 or 57 modulo 112 representable by x^2 + 448*y^2. 3
457, 569, 617, 809, 1289, 1801, 1913, 2153, 2297, 2473, 2521, 2633, 3049, 3257, 3929, 4057, 4153, 4201, 4937, 5209, 5273, 5881, 6073, 6553, 6841, 7177, 7193, 7417, 7529, 7673, 7753, 8009, 8521, 8537, 8681, 9769, 10889, 11257, 11321, 11369, 11593, 11657, 11897 (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. A325085 corresponds to those representable by the first form, and this sequence 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 7177:
- 7177 is a prime number,
- 7177 = 64*112 + 9,
- 7177 = 3^2 + 448*4^2,
- hence 7177 belongs to this sequence.
PROG
(PARI) See Links section.
CROSSREFS
See A325067 for similar results.
Cf. A325085.
Sequence in context: A068259 A036271 A061326 * A215895 A142828 A020364
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 28 2019
STATUS
approved

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Last modified February 21 22:13 EST 2024. Contains 370237 sequences. (Running on oeis4.)