A165288 Possible values of the difference between a cube and the largest square not larger than the cube.

0, 2, 4, 7, 11, 13, 19, 20, 26, 28, 35, 39, 40, 45, 47, 48, 49, 53, 55, 56, 60, 63, 67, 74, 76, 79, 81, 83, 100, 104, 107, 109, 116, 135, 139, 146, 147, 148, 150, 152, 155, 170, 174, 180, 184, 186, 191, 193, 200, 207, 212, 215, 216, 233, 235, 242, 244, 251, 270, 277

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Sep 13 2009

Keywords

• nonn

Comments

The values of A077116, sorted and duplicates removed.

Note that the values have been generated with a finite search radius and are not proved to be complete. [R. J. Mathar, Oct 09 2009]

Except for the leading 0, a subsequence of A229618 which is in turn (except for the initial 1) a subsequence of A106265. The values {15, 18, 25, 44, 54, 61, 71, 72, 87, 106, 112, 118, 126, 127,...} are in A229618 but not in the present sequence. Using results from A179386, it should be possible to prove that the sequence is complete up to a given point. - M. F. Hasler, Sep 26 2013

Examples

			The gap 0 appears in 1^3-1^2 or 4^3-8^2 etc.
The gap 2 appears for example in 3^3-5^2.
The gap 4 appears for example in 2^3-2^2 or 5^3-11^2.
The gap 19 appears in 7^3-18^2, the gap 20 in 6^3-14^2.
		

Crossrefs

Essentially the same as A087285.

Programs

Mathematica

lst={};Do[a=n^3-Floor[Sqrt[n^3]]^2;If[a<=508,AppendTo[lst,a]],{n,2*8!}]; Take[Union@lst,90]

Extensions

Edited by R. J. Mathar, Oct 09 2009

Name corrected by M. F. Hasler, Oct 05 2013