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A242285 Number of terms in the greedy sum for the n-th triangular number. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)