|
%I #17 Sep 10 2016 13:23:56
%S 0,2,4,8,11,13,16,17,18,22,23,26,29,31,32,34,36,44,46,50,52,58,59,62,
%T 64,68,72,73,79,88,89,92,98,99,100,104,116,117,118,121,122,124,128,
%U 134,136,137,139,143,144,146,153,158,162,169,173,176,178,184,187,196,198,199,200,207,208,211,221,223,226,232,234,236,239,242,244,248,253,256,261,268
%N Numbers of the form 4x^2+9xy-11y^2.
%C Discriminant 257.
%C 16*a(n) has the form z^2 - 257*y^2, where z = 8*x+9*y. [_Bruno Berselli_, Jun 20 2014]
%H R. J. Mathar, <a href="/A243181/b243181.txt">Table of n, a(n) for n = 1..2180</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)
%t maxTerm = 300; m0 = 10; dm = 10; Clear[f]; f[m_] := f[m] = Table[4*x^2 + 9 x*y - 11*y^2 , {x, -m, m}, {y, -m, m}] // Flatten // Union // Select[#, 0 <= # <= maxTerm&]&; f[m0]; f[m = m0]; While[f[m] != f[m - dm], m = m + dm]; f[m] (* _Jean-François Alcover_, Jun 04 2014 *) (* Brute force search, so not guaranteed to find all solutions, I believe. - _N. J. A. Sloane_, Jun 05 2014 *)
%t Reap[For[n = 0, n <= 30, n++,
%t If[Reduce[4*x^2 + 9*x*y - 11*y^2 == n, {x, y}, Integers] =!= False, Sow[n]]]][[2, 1]] (* Better program, not brute force, but slow. Confirms the terms up through 29. - _N. J. A. Sloane_, Jun 05 2014 *)
%Y Primes: A141168.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jun 02 2014
|
