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A243192 Nonnegative integers represented by the indefinite quadratic form 3x^2+3xy-4y^2. 2

%I #17 Jun 10 2014 16:52:19

%S 0,2,3,8,12,14,18,21,27,29,32,38,41,48,50,53,56,57,59,71,72,75,84,86,

%T 89,98,107,108,113,116,122,126,128,129,146,147,152,162,164,167,173,

%U 174,179,183,189,192,200,203,212,219,224,227,228,236,242,243,246,257

%N Nonnegative integers represented by the indefinite quadratic form 3x^2+3xy-4y^2.

%C Discriminant 57.

%C Note that 3*x^2+3*x*y-4*y^2=n is equivalent to 3*z^2 - 19*y^2=4*n where z=2*x+y. - _Robert Israel_, Jun 10 2014

%H Robert Israel, <a href="/A243192/b243192.txt">Table of n, a(n) for n = 1..3000</a>

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

%p select(m -> nops([isolve(3*z^2-19*y^2=4*m)])>0, [$0..1000]); # _Robert Israel_, Jun 10 2014

%t Reap[For[n = 0, n <= 30, n++, If[Reduce[3*x^2 + 3*x*y - 4*y^2 == n, {x, y}, Integers] =!= False, Sow[n]]]][[2, 1]]

%Y Cf. A243193. Primes: A141192.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jun 06 2014

%E More terms from _Colin Barker_, Jun 10 2014

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Last modified April 24 22:16 EDT 2024. Contains 371963 sequences. (Running on oeis4.)