A135790 Positive numbers of the form -x^4+6x^2 y^2-y^4 (where x,y are integers).

4, 7, 64, 112, 119, 164, 239, 324, 527, 567, 644, 959, 1024, 1519, 1792, 1904, 2047, 2500, 2624, 2884, 3479, 3824, 4207, 4324, 4375, 4879, 4964, 5184, 5572, 6647, 6887, 7327, 8119, 8432, 9072, 9604, 9639

Offset

1,1

Comments

Squares of these numbers are of the form N^4-M^2 (where N belongs to A135786 and M to A057102). Proof uses: (x^4 - 6x^2 y^2 + y^4)^2=(x^2+y^2)^4-(4(x^3y-xy^2))^2.

Refers to A057102, which had an incorrect description and has been replaced by A256418. As a result the present sequence should be re-checked. - N. J. A. Sloane, Apr 06 2015

Links

Table of n, a(n) for n=1..37.

Mathematica

a = {}; Do[Do[w = -x^4 + 6x^2 y^2 - y^4; If[w > 0&&w<10000, AppendTo[a, w]], {x, y, 2000}], {y, 1, 2000}]; Union[a]

Crossrefs

Cf. A000404, A050803, A057102, A135784, A060803, A135786, A135787, A135789.

Sequence in context: A330450 A060413 A065674 * A253202 A368271 A156474

Adjacent sequences: A135787 A135788 A135789 * A135791 A135792 A135793

Keyword

nonn

Author

Artur Jasinski, Nov 29 2007

Status

approved