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A242306
Number of terms in the squares-greedy sum for n.
3
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 11 2014
STATUS
approved