login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A141190 Primes of the form 2*x^2+4*x*y-5*y^2 (as well as of the form 2*x^2+8*x*y+y^2). 7
2, 11, 43, 67, 107, 113, 137, 163, 179, 193, 211, 233, 281, 331, 337, 347, 379, 401, 443, 449, 457, 491, 499, 547, 569, 571, 617, 641, 659, 673, 683, 739, 809, 827, 883, 907, 947, 953, 977, 1009, 1019, 1033, 1051, 1129, 1163, 1171, 1187, 1201, 1283, 1289 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant = 56. Class = 2. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1.

Also primes of the form x^6+6xy-5y^2. Cf. A243186. - N. J. A. Sloane, Jun 05 2014

REFERENCES

D. B. Zagier, Zetafunktionen und quadratische Koerper.

Z. I. Borevich and I. R. Shafarevich, Number Theory.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

EXAMPLE

a(3)=43 because we can write 43=2*4^2+4*4*1-5*1^2 (or 43=2*3^2+8*3*1+1^2).

MATHEMATICA

xy[{x_, y_}]:={2 x^2 + 4 x y - 5 y^2, 2 y^2 + 4 x y - 5 x^2}; Union[Select[Flatten[xy/@Subsets[Range[50], {2}]], #>0&&PrimeQ[#]&]] (* Vincenzo Librandi, Jun 09 2014 *)

CROSSREFS

Cf. A141191 (d=56) A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).

Cf. A243186.

For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Sequence in context: A219100 A140322 A027247 * A048500 A197189 A050620

Adjacent sequences:  A141187 A141188 A141189 * A141191 A141192 A141193

KEYWORD

nonn

AUTHOR

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (marcanmar(AT)alum.us.es), Jun 12 2008

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 July 8 17:40 EDT 2020. Contains 335524 sequences. (Running on oeis4.)