A242294 Number of terms in the greedy sum for n^3.

1, 2, 3, 4, 3, 3, 5, 3, 5, 6, 5, 4, 4, 6, 6, 5, 5, 3, 5, 6, 5, 6, 7, 5, 4, 6, 4, 5, 5, 5, 5, 6, 7, 5, 6, 7, 6, 4, 6, 3, 6, 7, 5, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 4, 5, 7, 7, 5, 7, 6, 6, 7, 7, 6, 6, 6, 7, 5, 5, 5, 6, 7, 7, 7, 6, 6, 5, 4, 6, 5, 6, 5

Offset

2,2

Comments

Greedy residues and related numbers are defined at A242293.

Links

Clark Kimberling, Table of n, a(n) for n = 2..2000

Example

n ... n^3 .. greedy sum
1 ..  1 .... (undefined)
2 ... 8 .... 1 = 1
3 ... 27 ... 9 = 8 + 1
4 ... 64 ... 36 = 27 + 8 + 1
5 ... 125 .. 100 = 64 + 27 + 8 + 1
6 ... 216 .. 216 = 125 + 64 + 27
7 ... 343 .. 342 = 216 + 125 + 1
8 ... 512 .. 504 = 343 + 125 + 27 + 8 + 1
9 ... 729 .. 729 = 512 + 216 + 1

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, A242295, A242296, A241833, A242284, A000578.

Sequence in context: A204932 A079086 A017839 * A234347 A328314 A286245

Adjacent sequences: A242291 A242292 A242293 * A242295 A242296 A242297

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2014

Status

approved