A135797 Numbers of the form x^4 + 6*x^2*y^2 + y^4 (where x,y are positive integers).

8, 41, 128, 136, 313, 353, 648, 656, 776, 1201, 1241, 1513, 2048, 2056, 2176, 2696, 3281, 3321, 3593, 4481, 5000, 5008, 5128, 5648, 7048, 7321, 7361, 7633, 8521

Offset: 1

Author

Artur Jasinski, Nov 29 2007

Keywords

• nonn
• more

Comments

Squares of these numbers are of the form N^4-M^2 (where N belongs to A135786 and M to A135796). Proof uses: (x^4+6*x^2*y^2+y^4)^2 = (x^2-y^2)^4+(4*x^3*y+4*x*y^3)^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Refers to A057102, which had an incorrect description and has been replaced by A256418.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

Crossrefs

Cf. A000404, A050803, A057102, A135784, A060803, A135786, A135787, A135789, A135790, A135791, A135792, A135793, A135795, A135796, A135796.

Programs

Mathematica

a = {}; Do[Do[w = x^4 + 6x^2 y^2 + y^4; If[w < 10000, AppendTo[a, w]], {x, y, 1000}], {y, 1, 1000}]; Union[a]
(* alternate program *)
Union[Select[#[[1]]^4+6#[[1]]^2 #[[2]]^2+#[[2]]^4&/@Tuples[Range[ 1000],2], #<10000&]] (* Harvey P. Dale, Oct 07 2012 *)