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. A325073 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.
Rémy Sigrist, PARI program for A325074
Wikipedia, Kaplansky's theorem on quadratic forms
EXAMPLE
Regarding 4409:
- 4409 is a prime number,
- 4409 = 220*20 + 9,
- 4409 = 53^2 + 100*4^2,
- hence 4409 belongs to this sequence.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 27 2019
STATUS
approved