A242296 Greedy-summable cubes.

216, 729, 2197, 2744, 5832, 6859, 15625, 19683, 21952, 59319, 64000, 68921, 85184, 97336, 117649, 185193, 300763, 474552, 551368, 658503, 729000, 778688, 804357, 970299, 1000000, 1092727, 1295029, 1481544, 1520875, 1860867, 1953125, 2197000, 2299968, 2352637

Offset

1,1

Comments

Greedy summability is defined at A242293.

Links

Clark Kimberling, Table of n, a(n) for n = 1..400

Example

Let s(n) = n^3 = A000578(n).  Then
a(1) =  216 = 125 + 64 + 27;
a(2) = 729 = 512 + 216 + 1;
a(3) = 2197 = 1728 + 343 + 125 + 1;
a(4) = 2744 = 2197 + 512 + 27 + 8.

Mathematica

z = 200;  s = Table[n^3, {n, 1, z}]; t = Table[{s[[n]], #, Total[#] == s[[n]]} &[DeleteCases[-Differences[FoldList[If[#1 - #2 >= 0, #1 - #2, #1] &, s[[n]], Reverse[Select[s, # < s[[n]] &]]]], 0]], {n, z}]
r[n_] := s[[n]] - Total[t[[n]][[2]]];
tr = Table[r[n], {n, 2, z}]  (* A242293 *)
c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242294 *)
f = 1 + Flatten[Position[tr, 0]]  (* A242295*)
f^3  (* A242296 *) (* Peter J. C. Moses, May 06 2014 *)

Crossrefs

Cf. A242293, A242294, A242295, A241833, A242284, A000578.

Sequence in context: A333316 A275154 A066890 * A223507 A135590 A187859

Adjacent sequences: A242293 A242294 A242295 * A242297 A242298 A242299

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2014

Status

approved