A325089 Prime numbers congruent to 49 or 121 modulo 240 representable by x^2 + 150*y^2.

601, 769, 2281, 2521, 2689, 3001, 5569, 5641, 5881, 6121, 6361, 6529, 6841, 7489, 8209, 8521, 9649, 9721, 11329, 12049, 12289, 12601, 13009, 14281, 14929, 15241, 16369, 17401, 17881, 18289, 19009, 19489, 19801, 20929, 21169, 21481, 21649, 21961, 22129, 22369

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. This sequence corresponds to those representable by the first form, and A325090 corresponds to those representable by the second form.

Links

Table of n, a(n) for n=1..40.

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 A325089

Wikipedia, Kaplansky's theorem on quadratic forms

Example

Regarding 5881:
- 5881 is a prime number,
- 5881 = 24*240 + 121,
- 5881 = 59^2 + 0*59*4 + 150*4^2,
- hence 5881 belongs to this sequence.

Prog

(PARI) See Links section.

Crossrefs

See A325067 for similar results.

Cf. A325090.

Sequence in context: A008689 A126835 A020370 * A050202 A031422 A359638

Adjacent sequences: A325086 A325087 A325088 * A325090 A325091 A325092

Keyword

nonn

Author

Rémy Sigrist, Mar 28 2019

Status

approved