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A243851 Irregular triangular array of denominators of the positive rational numbers ordered as in Comments. 4
1, 1, 1, 1, 2, 1, 2, 4, 1, 2, 4, 5, 5, 1, 2, 4, 5, 7, 5, 7, 2, 1, 2, 4, 5, 7, 5, 8, 7, 11, 11, 3, 7, 1, 2, 4, 5, 7, 5, 8, 7, 11, 11, 3, 13, 7, 13, 19, 16, 5, 11, 8, 1, 2, 4, 5, 7, 5, 8, 7, 11, 11, 3, 13, 7, 13, 19, 10, 16, 5, 11, 23, 8, 26, 20, 23, 6, 26, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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 denominators, by rows:  1,1,1,1,2,1,2,4,1,2,4,5,5,1,2,4,5,7,5,7,2.

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. A243852, A243853, A242488.

Sequence in context: A174843 A253572 A141539 * A168266 A059250 A303696

Adjacent sequences:  A243848 A243849 A243850 * A243852 A243853 A243854

KEYWORD

nonn,easy,tabf,frac

AUTHOR

Clark Kimberling, Jun 12 2014

STATUS

approved

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Last modified January 15 19:06 EST 2019. Contains 319171 sequences. (Running on oeis4.)