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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). 3
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

Same as A107008. -_ Arkadiusz Wesolowski_, Jul 25 2012

Discriminant = -96. Class = 4. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d = 4ac - b^2 and gcd(a,b,c)=1.

In x^2 + 8*x*y - 8*y^2, changing x to x - 4*y gives x^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.

D. B. Zagier, Zetafunktionen und quadratische Koerper.

LINKS

Table of n, a(n) for n=1..45.

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

Adjacent sequences:  A141372 A141373 A141374 * A141376 A141377 A141378

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

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Last modified February 26 01:41 EST 2020. Contains 332270 sequences. (Running on oeis4.)