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A319850 Number of distinct positive integers that can be obtained, starting with the initial interval partition (1, ..., n), by iteratively adding or multiplying together parts until only one part remains. 10
1, 2, 5, 21, 94, 446, 2287, 12568, 78509 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

The n-th row lists all integers that can be obtained starting with (1, ..., n):

  1

  2 3

  5 6 7 8 9

  9 10 11 12 13 14 15 16 17 18 19 20 21 24 25 26 27 28 30 32 36

MATHEMATICA

ReplaceListRepeated[forms_, rerules_]:=Union[Flatten[FixedPointList[Function[pre, Union[Flatten[ReplaceList[#, rerules]&/@pre, 1]]], forms], 1]];

Table[Length[Select[ReplaceListRepeated[{Range[n]}, {{foe___, x_, mie___, y_, afe___}:>Sort[Append[{foe, mie, afe}, x+y]], {foe___, x_, mie___, y_, afe___}:>Sort[Append[{foe, mie, afe}, x*y]]}], Length[#]==1&]], {n, 6}]

CROSSREFS

Cf. A000041, A001055, A001970, A048249, A066739, A066815, A070960, A201163, A318948, A318949, A319841.

Sequence in context: A152801 A062297 A047104 * A270597 A115087 A008981

Adjacent sequences:  A319847 A319848 A319849 * A319851 A319852 A319853

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 29 2018

STATUS

approved

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Last modified November 16 19:17 EST 2019. Contains 329201 sequences. (Running on oeis4.)