A325074 Prime numbers congruent to 9 modulo 20 representable by x^2 + 100*y^2.

109, 149, 269, 389, 409, 449, 569, 829, 929, 1069, 1129, 1429, 1489, 1609, 1889, 1949, 2129, 2269, 2309, 2549, 2609, 2689, 2749, 2789, 2909, 2969, 3109, 3209, 3229, 3449, 3709, 3769, 3889, 4129, 4349, 4409, 4889, 4909, 4969, 5189, 5309, 5449, 5569, 5749, 6029

Offset: 1

Author

Rémy Sigrist, Mar 27 2019

Keywords

• nonn

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.

Examples

			Regarding 4409:
- 4409 is a prime number,
- 4409 = 220*20 + 9,
- 4409 = 53^2 + 100*4^2,
- hence 4409 belongs to this sequence.
		

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

Crossrefs

See A325067 for similar results.

Cf. A141883, A325073.

Programs

PARI

See Links section.