

A243575


Irregular triangular array of numerators of the positive rational numbers ordered as in Comments.


3



1, 2, 3, 4, 5, 6, 7, 12, 12, 12, 8, 9, 10, 11, 16, 3, 12, 6, 4, 3, 40, 32, 13, 14, 15, 20, 3, 4, 6, 12, 15, 21, 19, 56, 26, 16, 11, 68, 52, 17, 18, 19, 24, 1, 12, 2, 12, 15, 21, 24, 9, 30, 33, 48, 23, 24, 34, 64, 47, 61, 35, 100, 46, 28, 19, 96, 72, 21, 22
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OFFSET

1,2


COMMENTS

Decree that (row 1) = (1,2,3). For n >=2, row n consists of numbers in increasing order generated as follows: x+4 for each x in row n1 together with 12/x for each nonzero x in row n1, where duplicates are deleted as they occur. Every rational number occurs exactly once in the array. The number of numbers in row n is A022095(n1) for n >= 4.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..5000


EXAMPLE

First 4 rows of the array of rationals:
1/1 .. 2/1 ... 3/1
4/1 .. 5/1 ... 6/2 . 7/1 . 12/1
12/7 . 12/5 .. 8/1 . 9/1 . 10/1 . 11/1 . 16/1
3/4 .. 12/11 . 6/5 . 4/3 . 3/2 .. 40/7 . 32/5 . 13/1 . 14/1 . 15/1 . 20/1
The numerators, by rows: 1,2,3,4,5,6,7,12,12,12,8,9,10,11,16,3,12,6,4,3,40,32,13,14,15,20.


MATHEMATICA

z = 10; g[1] = {1, 2, 3}; f1[x_] := x + 4; f2[x_] := 12/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[g[n], {n, 1, z}]
v = Flatten[u]
Denominator[v] (* A241837 *)
Numerator[v] (* A243575 *)


CROSSREFS

Cf. A241837, A243924, A022095.
Sequence in context: A178531 A175500 A222259 * A284447 A032985 A032869
Adjacent sequences: A243572 A243573 A243574 * A243576 A243577 A243578


KEYWORD

nonn,easy,tabf,frac


AUTHOR

Clark Kimberling, Jun 15 2014


STATUS

approved



