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.

1, 2, 5, 21, 94, 446, 2287, 12568, 78509

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: A062297 A357791 A047104 * A270597 A174080 A337283

Adjacent sequences: A319847 A319848 A319849 * A319851 A319852 A319853

Keyword

nonn,more

Author

Gus Wiseman, Sep 29 2018

Status

approved