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A242259 Number of summands in s-greedy sum of s(n), where s(n) = A000009(n) (strict partition numbers). 2
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 4, 4, 3, 2, 4, 4, 3, 3, 4, 4, 3, 2, 4, 4, 4, 3, 4, 4, 4, 4, 5, 4, 4, 3, 3, 4, 5, 4, 4, 4, 4, 4, 4, 3, 5, 4, 5, 5, 4, 4, 5, 3, 5, 4, 5, 5, 5, 5, 4, 5, 4, 3, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

See A242252 for the definitions of greedy sum and summability.  Conjecture:  A000009(n) is A000009-greedy summable for n >= 3.

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

1 ... 1 ...... (undefined)

2 ... 2 ...... (undefined)

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

4 ... 2 .......2 ........ 1 + 1

5 ... 3 .......2 .......  2 + 1

6 ... 4 ...... 2 ........ 3 + 1

7 ... 5 ...... 2 ........ 4 + 1

8 ... 6 ...... 2 ........ 5 + 1

9 ... 8 ...... 2 ........ 6 + 2

10 .. 10 ..... 2 ........ 8 + 2

25 .. 142 .... 3 ........ 122 + 18 + 2

35 .. 585 .... 4 ........ 512 + 64 + 8 + 1

55 .. 6378 ... 5 ........ 5718 + 585 + 64 + 10 + 1

LINKS

Clark Kimberling, Table of n, a(n) for n = 3..999

EXAMPLE

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

1 ... 1 ...... (undefined)

2 ... 2 ...... (undefined)

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

4 ... 2 .......2 ........ 1 + 1

5 ... 3 .......2 .......  2 + 1

6 ... 4 ...... 2 ........ 3 + 1

7 ... 5 ...... 2 ........ 4 + 1

8 ... 6 ...... 2 ........ 5 + 1

9 ... 8 ...... 2 ........ 6 + 2

10 .. 10 ..... 2 ........ 8 + 2

25 .. 142 .... 3 ........ 122 + 18 + 2

35 .. 585 .... 4 ........ 512 + 64 + 8 + 1

55 .. 6378 ... 5 ........ 5718 + 585 + 64 + 10 + 1

MATHEMATICA

z = 200;  s = Table[PartitionsQ[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. A242258, A241833, A242252, A000009.

Sequence in context: A168353 A053230 A194334 * A048766 A105516 A105518

Adjacent sequences:  A242256 A242257 A242258 * A242260 A242261 A242262

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 10 2014

STATUS

approved

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)