

A237351


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


11



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.


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).


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 A126471 A317100
Adjacent sequences: A237348 A237349 A237350 * A237352 A237353 A237354


KEYWORD

nonn


AUTHOR

Colin Barker, Feb 06 2014


STATUS

approved



