login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

(PARI) See Links section.

CROSSREFS

See A325067 for similar results.

Cf. A325087.

Sequence in context: A142918 A139502 A140629 * A321582 A137771 A108831

Adjacent sequences:  A325085 A325086 A325087 * A325089 A325090 A325091

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Mar 28 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 19 21:19 EDT 2019. Contains 326133 sequences. (Running on oeis4.)