proposed

approved

editing

proposed

allocated Number of terms in the squares-greedy sum for Clark Kimberlingn.

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

2,4

Greedy sums and related numbers are defined at A242305.

Clark Kimberling, <a href="/A242306/b242306.txt">Table of n, a(n) for n = 2..2000</a>

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

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 *)

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

allocated

nonn,easy

Clark Kimberling, May 11 2014

approved

editing

allocated for Clark Kimberling

allocated

approved