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Numbers of the form 8x^2+xy-8y^2.
3

%I #25 Mar 07 2020 14:57:36

%S 0,1,4,8,9,16,22,25,26,32,34,36,44,46,49,52,58,61,62,64,67,68,72,81,

%T 88,92,100,104,113,116,118,121,124,128,136,143,144,146,157,158,169,

%U 176,178,184,187,193,196,197,198,200,208,221,225,227,232,234,236,241,242,244,248,253,256,257,268,272,274,278,286,288,289,292,299,306,316,319,324,338,341

%N Numbers of the form 8x^2+xy-8y^2.

%C Discriminant 257.

%C 32*a(n) has the form z^2 - 257*y^2, where z = 16*x+y. [_Bruno Berselli_, Jun 20 2014]

%H R. J. Mathar, <a href="/A243180/b243180.txt">Table of n, a(n) for n = 1..1676</a>

%H Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BinaryQuadraticForms#Implementation">Binary Quadratic Forms</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 = 400; m0 = 10; dm = 10; Clear[f]; f[m_] := f[m] = Table[8*x^2 + x*y - 8*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 *)

%o (Sage) # uses[binaryQF]

%o # The function binaryQF is defined in the link 'Binary Quadratic Forms'.

%o Q = binaryQF([8, 1, -8])

%o print([0]+Q.represented_positives(341)) # _Peter Luschny_, Oct 26 2016

%Y Primes: A141167. Cf. A243181, A141168.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jun 02 2014