A325090 Prime numbers congruent to 49 or 121 modulo 240 representable by x^2 + 960*y^2.

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

Table of n, a(n) for n=1..39.

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 A325090

Wikipedia, Kaplansky's theorem on quadratic forms

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

Adjacent sequences: A325087 A325088 A325089 * A325091 A325092 A325093

Keyword

nonn

Author

Rémy Sigrist, Mar 28 2019

Status

approved