A242295 Positive integers k for which k^3 is greedy-summable.

6, 9, 13, 14, 18, 19, 25, 27, 28, 39, 40, 41, 44, 46, 49, 57, 67, 78, 82, 87, 90, 92, 93, 99, 100, 103, 109, 114, 115, 123, 125, 130, 132, 133, 135, 140, 150, 151, 160, 165, 169, 173, 182, 188, 193, 204, 208, 209, 211, 214, 217, 224, 230, 237, 238, 240, 244

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) = 6; s(6) = 216 = 125 + 64 + 27;
a(2) = 9; s(9) = 729 = 512 + 216 + 1;
a(3) = 13; s(13) = 2197 = 1728 + 343 + 125 + 1;
a(4) = 14; s(14) = 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, A242296, A241833, A242284, A000578.

Sequence in context: A263773 A242874 A284800 * A064799 A236763 A030499

Adjacent sequences: A242292 A242293 A242294 * A242296 A242297 A242298

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2014

Status

approved