%I #25 Apr 23 2023 13:24:20

%S 3,5,12,17,20,21,27,35,41,45,47,48,59,68,75,80,83,84,89,101,108,111,

%T 119,125,129,131,140,147,153,164,167,173,180,185,188,189,192,201,215,

%U 227,236,237,243,245,251,255,257,269,272,287,293,300,311,315,320,327

%N Positive integers k such that x^2 - 5xy + y^2 + k = 0 has integer solutions.

%C See comments on method used in A084917.

%C The equivalent sequence for x^2 - 3xy + y^2 + k = 0 is A031363.

%C The equivalent sequence for x^2 - 4xy + y^2 + k = 0 is A084917.

%C Positive numbers of the form 3x^2 - 7y^2. - _Jon E. Schoenfield_, Jun 03 2022

%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)

%e 12 is in the sequence because x^2 - 5xy + y^2 + 12 = 0 has integer solutions, for example, (x, y) = (2, 8).

%t Select[Range[350],Length[FindInstance[x^2-5x y+y^2+#==0,{x,y},Integers]]>0&] (* _Harvey P. Dale_, Apr 23 2023 *)

%Y Cf. A004253 (k = 3), A237254 (k = 5), A237255 (k = 17).

%Y Cf. A031363, A084917.

%Y For primes see A141160.

%K nonn

%O 1,1

%A _Colin Barker_, Feb 06 2014