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

Author

Gus Wiseman, Sep 29 2018

Keywords

• nonn
• more

Examples

			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
		

Crossrefs

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

Programs

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}]