A237351 - OEIS

A237351

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

3, 5, 12, 17, 20, 21, 27, 35, 41, 45, 47, 48, 59, 68, 75, 80, 83, 84, 89, 101, 108, 111, 119, 125, 129, 131, 140, 147, 153, 164, 167, 173, 180, 185, 188, 189, 192, 201, 215, 227, 236, 237, 243, 245, 251, 255, 257, 269, 272, 287, 293, 300, 311, 315, 320, 327

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OFFSET

1,1

COMMENTS

See comments on method used in A084917.

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

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

Positive numbers of the form 3x^2 - 7y^2. - Jon E. Schoenfield, Jun 03 2022

LINKS

Table of n, a(n) for n=1..56.

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

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

Cf. A031363, A084917.

For primes see A141160.

Sequence in context: A032438 A025083 A203150 * A299490 A361274 A126471

Adjacent sequences: A237348 A237349 A237350 * A237352 A237353 A237354

KEYWORD

nonn

AUTHOR

Colin Barker, Feb 06 2014

STATUS

approved