login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A141375 Primes of the form x^2 + 8*x*y - 8*y^2 (as well as of the form x^2 + 10*x*y + y^2). 4
73, 97, 193, 241, 313, 337, 409, 433, 457, 577, 601, 673, 769, 937, 1009, 1033, 1129, 1153, 1201, 1249, 1297, 1321, 1489, 1609, 1657, 1753, 1777, 1801, 1873, 1993, 2017, 2089, 2113, 2137, 2161, 2281, 2377, 2473, 2521, 2593, 2617, 2689, 2713, 2833, 2857 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Conjecture: Same as A107008. - Arkadiusz Wesolowski, Jul 25 2012
Discriminant = +96.
x^2 + 8*x*y - 8*y^2 = (x+4*y)^2 - 24*y^2, and x^2 + 10*x*y + y^2 = (x+5*y)^2 - 24*y^2, so this sequence is also primes of the form x^2 - 24*y^2. - Michael Somos, Jun 05 2013
REFERENCES
Z. I. Borevich and I. R. Shafarevich. Number Theory. Academic Press. 1966.
LINKS
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
EXAMPLE
a(1) = 73 because we can write 73 = 5^2 + 8*5*2 - 8*2^2 (or 73 = 2^2 + 10*2*3 + 3^2).
MATHEMATICA
Union[Select[Flatten[Table[x^2 + 8*x*y - 8*y^2, {x, 40}, {y, 40}]], # > 0 && PrimeQ[#] &]] (* T. D. Noe, Jun 12 2013 *)
CROSSREFS
Cf. A107008, A141373, A107003, A141376 (d = -96).
Sequence in context: A268426 A155573 A107008 * A140621 A143577 A146354
KEYWORD
nonn
AUTHOR
Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 28 2008
EXTENSIONS
More terms and offset corrected by Arkadiusz Wesolowski, Jul 25 2012
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)