A165288 - OEIS

%I #15 Oct 09 2013 03:55:23

%S 0,2,4,7,11,13,19,20,26,28,35,39,40,45,47,48,49,53,55,56,60,63,67,74,

%T 76,79,81,83,100,104,107,109,116,135,139,146,147,148,150,152,155,170,

%U 174,180,184,186,191,193,200,207,212,215,216,233,235,242,244,251,270,277

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

%C The values of A077116, sorted and duplicates removed.

%C 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]

%C 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

%e The gap 0 appears in 1^3-1^2 or 4^3-8^2 etc.

%e The gap 2 appears for example in 3^3-5^2.

%e The gap 4 appears for example in 2^3-2^2 or 5^3-11^2.

%e The gap 19 appears in 7^3-18^2, the gap 20 in 6^3-14^2.

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

%Y Essentially the same as A087285.

%K nonn

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Sep 13 2009

%E Edited by _R. J. Mathar_, Oct 09 2009

%E Name corrected by _M. F. Hasler_, Oct 05 2013