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A243852 Irregular triangular array of numerators of the positive rational numbers ordered as in Comments. 4
1, 3, 2, 4, 3, 5, 5, 3, 6, 7, 7, 6, 3, 7, 9, 11, 11, 12, 8, 6, 1, 8, 11, 15, 16, 19, 13, 15, 13, 15, 12, 2, 3, 9, 13, 19, 21, 26, 18, 23, 20, 26, 23, 5, 21, 10, 15, 21, 15, 4, 6, 3, 10, 15, 23, 26, 33, 23, 31, 27, 37, 34, 8, 34, 17, 28, 40, 21, 31, 9, 17, 33 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

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

EXAMPLE

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.

MATHEMATICA

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 *)

CROSSREFS

Cf. A243851, A243853, A242488.

Sequence in context: A119707 A052938 A140114 * A025532 A195459 A133131

Adjacent sequences:  A243849 A243850 A243851 * A243853 A243854 A243855

KEYWORD

nonn,easy,tabf,frac

AUTHOR

Clark Kimberling, Jun 12 2014

STATUS

approved

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Last modified December 13 00:17 EST 2017. Contains 295954 sequences.