A243930 - OEIS

%I #4 Jun 19 2014 11:19:05

%S 1,2,3,4,6,6,9,15,23,34,48,71,102,155,232,348,519,765,1140,1691,2528,

%T 3789,5634,8396,12527,18709,27955,41755,62410,93227,139239,207939,

%U 310603,464212,694207

%N Number of numbers in row n of the array at A243928.

%C Decree that (row 1) = (1).  For n >=2, row n consists of numbers in increasing order generated as follows:  x+1 for each x in row n-1 together with -2/x for each nonzero x in row n-1, where duplicates are deleted as they occur.  The number of numbers in row n is A243930(n).   Conjecture:  every rational number occurs exactly once in the array.

%e First 7 rows of the array of rationals:

%e 1/1

%e -3/1 .. 2/1

%e -2/1 .. -3/2 .. 3/1

%e -1/1 .. -1/2 .. 3/2 ... 4/1

%e -3/4 .. 0/1 ... 1/2 ... 5/2 .. 5/1 .. 6/1

%e -6/1 .. -6/5 .. -3/5 .. 1/4 .. 7/2 .. 7/1

%e -12/1 . -5/1 .. -6/7 .. -3/7 . -1/5 . 2/5 . 5/4 . 9/2 . 8/1, so that the first 7 terms of A243930 are 1,2,3,4,6,6,9.

%t z = 20; g[1] = {1}; f1[x_] := x + 1; f2[x_] := -3/x; h[1] = g[1];

%t b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]]]];

%t h[n_] := h[n] = Union[h[n - 1], g[n - 1]]; g[n_] := g[n] = Complement[b[n], Intersection[b[n], h[n]]]; g[6] = Delete[g[6], 7];

%t Table[Length[g[n]], {n, 1, z}]  (* A243930 *)

%Y Cf. A243927.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 15 2014