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A141338 Primes of the form x^2+9*x*y-3*y^2 (as well as of the form 7*x^2+11*x*y+y^2). 2

%I #16 Feb 19 2022 07:53:35

%S 7,19,31,67,97,103,109,157,163,193,211,283,307,349,373,379,397,421,

%T 439,541,547,577,607,661,691,727,733,751,769,811,853,877,907,919,937,

%U 997,1033,1039,1051,1063,1087,1093,1117,1123,1213,1237,1249,1279,1291,1303

%N Primes of the form x^2+9*x*y-3*y^2 (as well as of the form 7*x^2+11*x*y+y^2).

%C Discriminant = 93. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.

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

%H N. J. A. Sloane et al., <a href="/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a>: Index to related sequences, programs, references. OEIS wiki, June 2014.

%H D. B. Zagier, <a href="https://doi.org/10.1007/978-3-642-61829-1">Zetafunktionen und quadratische Körper</a>, Springer, 1981.

%e a(2) = 19 because we can write 19 = 2^2 + 9*2*5 - 3*5^2 (or 19 = 7*1^2 + 11*1*1 + 1^2).

%Y Cf. A141339 (d=93).

%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 25 2008

%E More terms from _Colin Barker_, Apr 05 2015

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Last modified April 24 13:38 EDT 2024. Contains 371957 sequences. (Running on oeis4.)