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

1,2

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

Links

Table of n, a(n) for n=1..60.

Example

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.

Mathematica

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

Crossrefs

Essentially the same as A087285.

Sequence in context: A356133 A191323 A307207 * A327572 A370905 A362946

Adjacent sequences: A165285 A165286 A165287 * A165289 A165290 A165291

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Sep 13 2009

Extensions

Edited by R. J. Mathar, Oct 09 2009

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

Status

approved