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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

%I

%S 73,97,193,241,313,337,409,433,457,577,601,673,769,937,1009,1033,1129,

%T 1153,1201,1249,1297,1321,1489,1609,1657,1753,1777,1801,1873,1993,

%U 2017,2089,2113,2137,2161,2281,2377,2473,2521,2593,2617,2689,2713,2833,2857

%N 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).

%C Same as A107008. [Arkadiusz Wesolowski, Jul 25 2012]

%C 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.

%C 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

%D Borevich and Shafarevich, Number Theory.

%D D. B. Zagier, Zetafunktionen und quadratische Koerper.

%e 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).

%t Union[Select[Flatten[Table[x^2 + 8*x*y - 8*y^2, {x, 40}, {y, 40}]], # > 0 && PrimeQ[#] &]] (* _T. D. Noe_, Jun 12 2013 *)

%Y Cf. A141373, A141374, A141376 (d = -96).

%K nonn

%O 1,1

%A 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

%E More terms and offset corrected by Arkadiusz Wesolowski, Jul 25 2012

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Last modified December 9 04:45 EST 2016. Contains 278960 sequences.