A325073 Prime numbers congruent to 9 modulo 20 representable by x^2 + 20*y^2.

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

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

Table of n, a(n) for n=1..45.

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 A325073

Wikipedia, Kaplansky's theorem on quadratic forms

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.

Cf. A141883, A325074.

Sequence in context: A308787 A141883 A142791 * A152294 A201487 A317537

Adjacent sequences: A325070 A325071 A325072 * A325074 A325075 A325076

Keyword

nonn

Author

Rémy Sigrist, Mar 27 2019

Status

approved