

A243925


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


6



1, 1, 1, 1, 1, 3, 1, 1, 2, 3, 1, 1, 5, 2, 3, 1, 1, 1, 2, 3, 5, 2, 3, 1, 3, 1, 3, 7, 7, 5, 3, 5, 2, 3, 1, 3, 4, 5, 5, 4, 7, 7, 5, 3, 5, 2, 3, 1, 1, 5, 7, 5, 13, 7, 13, 9, 5, 4, 7, 7, 7, 5, 3, 5, 2, 3, 1, 1, 1, 3, 5, 4, 6, 6, 4, 9, 9, 7, 8, 5, 13, 7, 13, 9, 5
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OFFSET

1,6


COMMENTS

Decree that (row 1) = (1). For n >=2, row n consists of numbers in increasing order generated as follows: x+1 for each x in row n1 together with 2/x for each nonzero x in row n1, where duplicates are deleted as they occur. The number of numbers in row n is A243927(n). Conjecture: every rational number occurs exactly once in the array.


LINKS



EXAMPLE

First 7 rows of the array of rationals:
1/1
2/1 ... 2/1
1/1 ... 3/1
2/3 ... 0/1 ... 4/1
1/2 ... 1/3 ... 5/1
6/1 ... 2/5 .. 1/2 ... 4/3 ... 6/1
5/1 ... 4/1 .. 3/2 .. 1/3 .. 3/5 .. 3/2 .. 7/3 .. 7/1
The denominators, by rows: 1,1,1,1,1,3,1,1,2,3,1,1,5,2,3,1,1,1,2,3,5,2,3,1.


MATHEMATICA

z = 13; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 2/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 = Delete[Flatten[u], 12]


CROSSREFS



KEYWORD

nonn,easy,tabf,frac


AUTHOR



STATUS

approved



