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A325090
Prime numbers congruent to 49 or 121 modulo 240 representable by x^2 + 960*y^2.
3
1009, 1249, 1321, 1489, 1801, 3169, 3889, 4129, 4201, 4441, 7321, 7561, 8689, 8761, 8929, 9001, 9241, 10369, 11161, 12841, 13249, 13729, 14449, 15649, 15889, 16921, 17569, 18049, 18121, 19081, 19249, 20521, 21001, 24049, 24121, 24841, 25561, 25801, 25969
OFFSET
1,1
COMMENTS
Brink showed that prime numbers congruent to 49 or 121 modulo 240 are representable by exactly one of the quadratic forms x^2 + 150*y^2 or x^2 + 960*y^2. A325089 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 9001:
- 9001 is a prime number,
- 9001 = 37*240 + 121,
- 9001 = 19^2 + 960*3^2,
- hence 9001 belongs to this sequence.
PROG
(PARI) See Links section.
CROSSREFS
See A325067 for similar results.
Cf. A325089.
Sequence in context: A153640 A139665 A261405 * A024974 A025400 A182695
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 28 2019
STATUS
approved