A135797 Numbers of the form x^4 + 6x^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

1,1

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+6x^2y^2+y^4)^2=(x^2-y^2)^4+(4x^3y+4x*y^3)^2(*Artur Jasinski*)

Refers to A057102, which had an incorrect description and has been replaced by A256418.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..29.

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] (*Artur Jasinski*)
Union[Select[#[[1]]^4+6#[[1]]^2 #[[2]]^2+#[[2]]^4&/@Tuples[Range[ 1000], 2], #<10000&]] (* Harvey P. Dale, Oct 07 2012 *)

Crossrefs

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

Sequence in context: A041116 A326286 A250322 * A171714 A342034 A304160

Adjacent sequences: A135794 A135795 A135796 * A135798 A135799 A135800

Keyword

nonn

Author

Artur Jasinski, Nov 29 2007

Status

approved