A319850 - OEIS

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.

%I #5 Sep 30 2018 20:26:56

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

%N 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.

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

%e 1

%e 2 3

%e 5 6 7 8 9

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

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

%t 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}]

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

%K nonn,more

%O 1,2

%A _Gus Wiseman_, Sep 29 2018