

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
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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 n1 together with 4/x for each x in row n1, 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: A211174 A059833 A123152 * A267185 A065187 A185511
Adjacent sequences: A243852 A243853 A243854 * A243856 A243857 A243858


KEYWORD

nonn,easy,tabf,frac


AUTHOR

Clark Kimberling, Jun 12 2014


STATUS

approved



