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A325073 Prime numbers congruent to 9 modulo 20 representable by x^2 + 20*y^2. 3
29, 89, 229, 349, 509, 709, 769, 809, 1009, 1049, 1109, 1229, 1249, 1289, 1409, 1549, 1669, 1709, 1789, 2029, 2069, 2089, 2389, 2729, 3049, 3089, 3169, 3329, 3389, 3469, 3529, 3929, 3989, 4049, 4229, 4289, 4549, 4649, 4729, 4789, 5009, 5209, 5669, 5689, 5849 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Brink showed that prime numbers congruent to 9 modulo 20 are representable by exactly one of the quadratic forms x^2 + 20*y^2 or x^2 + 100*y^2. This sequence corresponds to those representable by the first form, and A325074 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 1009:
- 1009 is a prime number,
- 1009 = 50*20 + 9,
- 1009 = 17^2 + 20*6^2,
- hence 1009 belongs to this sequence.
PROG
(PARI) See Links section.
CROSSREFS
See A325067 for similar results.
Sequence in context: A308787 A141883 A142791 * A152294 A201487 A317537
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 27 2019
STATUS
approved

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Last modified June 14 08:50 EDT 2024. Contains 373393 sequences. (Running on oeis4.)