A325088 - OEIS

A325088

Prime numbers congruent to 1 or 169 modulo 240 representable neither by x^2 + 150*y^2 nor by x^2 + 960*y^2.

241, 409, 1201, 1609, 2089, 2161, 3049, 3121, 3529, 4561, 4729, 4969, 5281, 6481, 6961, 7129, 7369, 7681, 8089, 8161, 9049, 11689, 12241, 12721, 12889, 13441, 13921, 14401, 16249, 17449, 17929, 19441, 19609, 19681, 20161, 20641, 20809, 21121, 21841, 23041

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OFFSET

1,1

COMMENTS

Brink showed that prime numbers congruent to 1 or 169 modulo 240 are representable by both or neither of the quadratic forms x^2 + 150*y^2 and x^2 + 960*y^2. A325087 corresponds to those representable by both, and this sequence corresponds to those representable by neither.

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 A325088

Wikipedia, Kaplansky's theorem on quadratic forms

EXAMPLE

Regarding 241:

- 241 is a prime number,

- 241 = 1*240 + 1,

- 241 is neither representable by x^2 + 150*y^2 nor by x^2 + 960*y^2,

- hence 241 belongs to this sequence.

PROG