1,2

Decree that (row 1) = (1) and (row 2) = (3,2). For n >= 4, row n consists of numbers in decreasing order generated as follows: x+1 for each x in row n-1 together with 3/x for each x in row n-1, and duplicates are rejected as they occur. Every positive rational number occurs exactly once in the resulting array.

Clark Kimberling, Table of n, a(n) for n = 1..3000

First 6 rows of the array of rationals:

1/1

3/1 ... 2/1

4/1 ... 3/2

5/1 ... 5/2 ... 3/4

6/1 ... 7/2 ... 7/4 ... 6/5 ... 3/5

7/1 ... 9/2 ... 11/4 .. 11/5 .. 12/7 .. 8/5 .. 6/7 .. 1/2

The numerators, by rows: 1,3,2,4,3,5,5,3,6,7,7,6,3,7,9,11,11,12,8,6,1.

z = 12; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 3/x; h[1] = g[1];

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

h[n_] := h[n] = Union[h[n - 1], g[n - 1]];

g[n_] := g[n] = Complement [b[n], Intersection[b[n], h[n]]]

u = Table[Reverse[g[n]], {n, 1, z}]; v = Flatten[u];

Denominator[v] (* A243851 *)

Numerator[v] (* A243852 *)

Table[Length[g[n]], {n, 1, z}] (* A243853 *)

Cf. A243851, A243853, A242488.

Sequence in context: A052938 A302391 A140114 * A373701 A025532 A329584

Adjacent sequences: A243849 A243850 A243851 * A243853 A243854 A243855

nonn,easy,tabf,frac

Clark Kimberling, Jun 12 2014

approved