A242306 Number of terms in the squares-greedy sum for n.

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

Offset

2,4

Comments

Greedy sums and related numbers are defined at A242305.

Links

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

Example

n ... squares-greedy sum for n
1 ... (undefined)
2 ... 1 = 1
3 ... 1 = 1
4 ... 1 = 1
5 ... 5 = 4 + 1
6 ... 5 = 4 + 1
7 ... 5 = 4 + 1
8 ... 5 = 4 + 1
9 ... 5 = 4 + 1
10 .. 10 = 9 + 1
11 .. 10 = 9 + 1
12 .. 10 = 9 + 1
13 .. 13 =  9 + 4
14 .. 14 = 9 + 4 + 1

Mathematica

z = 200;  s = Table[n^2, {n, 1, z}]; s1 = Table[n, {n, 1, z}]; t = Table[{s1[[n]], #, Total[#] == s1[[n]]} &[DeleteCases[-Differences[FoldList[If[#1 - #2 >= 0, #1 - #2, #1] &, s1[[n]],
Reverse[Select[s, # < s1[[n]] &]]]], 0]], {n, z}]
r[n_] := s1[[n]] - Total[t[[n]][[2]]];
tr = Table[r[n], {n, 2, z}]  (* A242305 *)
c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242306 *)
f = 1 + Flatten[Position[tr, 0]]  (* A242307 *)  (* Peter J. C. Moses, May 06 2014 *)

Crossrefs

Cf. A242305, A242307, A241833, A000027, A000290.

Sequence in context: A131841 A309432 A230261 * A245636 A171622 A351846

Adjacent sequences: A242303 A242304 A242305 * A242307 A242308 A242309

Keyword

nonn,easy

Author

Clark Kimberling, May 11 2014

Status

approved