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A242258 Number of summands in s-greedy sum of s(n), where s(n) = A000041(n), the partitions numbers. 2
1, 2, 2, 2, 3, 3, 2, 3, 3, 3, 4, 3, 4, 3, 4, 4, 3, 4, 3, 3, 5, 3, 4, 5, 5, 4, 5, 5, 4, 4, 6, 5, 5, 4, 4, 5, 5, 6, 5, 5, 4, 7, 6, 6, 7, 6, 6, 5, 6, 5, 7, 5, 6, 7, 7, 7, 8, 7, 7, 6, 6, 6, 7, 7, 8, 6, 6, 7, 7, 7, 7, 8, 7, 8, 8, 7, 7, 8, 6, 6, 8, 8, 8, 7, 5, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

See A242252 for the definitions of greedy sum and summability.  Conjecture:  A000041(n) is A000041-greedy summable for n >= 3.

LINKS

Clark Kimberling, Table of n, a(n) for n = 2..1000

EXAMPLE

n... s(n) .. a(n) .... s-greedy sum for s(n)

1 ... 1 .... (none).. (undefined)

2 ... 2 .... 1 ....... 1

3 ... 3 .... 2 ....... 2 + 1

4 ... 5 .... 2 ....... 3 + 2

5 ... 7 .... 2 ....... 5 + 2

6 ... 10 ... 3 ....... 7 + 3 + 1

7 ... 15 ... 3 ....... 11 + 3 + 1

8 ... 22 ... 2 ....... 15 + 7

9 ... 30 ... 3 ....... 22 + 7 + 1

10 .. 42 ... 3 ....... 33 + 11 + 1

11 .. 56.... 4 ....... 42 + 11 + 3

12 .. 77.... 3 ....... 56 + 11 + 5 + 1

MATHEMATICA

z = 200;  s = Table[PartitionsP[n], {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]]]; c =  Table[Length[t[[n]][[2]]], {n, 2, z}] (* Peter J. C. Moses, May 06 2014 *)

CROSSREFS

Cf. A242259, A241833, A242252, A000041.

Sequence in context: A165924 A212628 A272851 * A232615 A257177 A243423

Adjacent sequences:  A242255 A242256 A242257 * A242259 A242260 A242261

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 10 2014

STATUS

approved

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Last modified January 29 01:49 EST 2020. Contains 331328 sequences. (Running on oeis4.)