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A243855 Irregular triangular array of numerators of the positive rational numbers ordered as in Comments. 4
1, 4, 2, 5, 3, 6, 4, 4, 7, 7, 9, 2, 8, 10, 14, 20, 12, 5, 4, 9, 13, 19, 29, 19, 8, 12, 11, 10, 6, 1, 10, 16, 24, 38, 26, 11, 17, 18, 28, 17, 11, 3, 28, 36, 20, 12, 4, 11, 19, 29, 47, 33, 14, 22, 25, 39, 24, 16, 5, 47, 65, 39, 25, 20, 28, 14, 13, 20, 12, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Decree that (row 1) = (1).  For n >= 2, row n consists of numbers in decreasing order generated as follows:  x+1 for each x in row n-1 together with 4/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

4/1 ... 2/1

5/1 ... 3/1

6/1 ... 4/3 ... 4/5

7/1 ... 7/3 ... 9/5 ... 2/3

8/1 ... 10/3 ... 14/5 .. 20/9 .. 12/7 .. 5/3 .. 4/7

The numerators, by rows:  1,4,2,5,3,6,4,4,,7,7,9,2,8,10,14,20,12,5,4.

MATHEMATICA

z = 12; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 4/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] (* A243854 *)

Numerator[v]   (* A243855 *)

Table[Length[g[n]], {n, 1, z}] (* A243856 *)

CROSSREFS

Cf. A243854, A243856, A242488, A243848.

Sequence in context: A059833 A123152 A309567 * A267185 A065187 A185511

Adjacent sequences:  A243852 A243853 A243854 * A243856 A243857 A243858

KEYWORD

nonn,easy,tabf,frac

AUTHOR

Clark Kimberling, Jun 12 2014

STATUS

approved

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Last modified December 1 11:38 EST 2021. Contains 349429 sequences. (Running on oeis4.)