A242285 Number of terms in the greedy sum for the n-th triangular number.

1, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 4, 2, 3, 3, 3, 4, 4, 3, 2, 3, 3, 3, 4, 4, 3, 4, 2, 3, 3, 3, 4, 4, 3, 4, 4, 2, 3, 3, 3, 4, 4, 3, 4, 4, 4, 2, 3, 3, 3, 4, 4, 3, 4, 4, 4, 3, 2, 3, 3, 3, 4, 4, 3, 4, 4, 4, 3, 4, 2, 3, 3, 3, 4, 4, 3, 4, 4, 4

Offset

2,2

Comments

Greedy residues and related numbers are defined at A242284.

Links

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

Example

n ... n(n+1)/2 ... greedy sum for n(n+1)/2
1 ..  1 .......... (undefined)
2 ... 3 .......... 1 = 1
3 ... 6 .......... 4 = 3 + 1
4 ... 10 ......... 10 = 6 + 3 + 1
5 ... 15 ......... 14 = 10 + 3 + 1
6 ... 21 ......... 21 = 15 + 6
7 ... 28 ......... 28 = 21 + 6 + 1
8 ... 36 ......... 35 = 28 + 6 + 1

Mathematica

z = 200;  s = Table[n (n + 1)/2, {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}]  (* A242284 *)
c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242285 *)
f = 1 + Flatten[Position[tr, 0]]  (* A242286 *)
f (f + 1)/2  (* A242287 *) (* Peter J. C. Moses, May 06 2014 *)

Crossrefs

Cf. A242284, A242286, A242287, A241833, A000217.

Sequence in context: A262955 A276859 A007538 * A238756 A025076 A110006

Adjacent sequences: A242282 A242283 A242284 * A242286 A242287 A242288

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2014

Status

approved