|
|
A243714
|
|
Irregular triangular array of denominators of all rational numbers ordered as in Comments.
|
|
5
|
|
|
1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 3, 2, 1, 2, 3, 5, 4, 3, 2, 1, 3, 5, 5, 6, 3, 5, 4, 3, 2, 1, 1, 4, 7, 8, 7, 7, 5, 5, 6, 3, 5, 4, 3, 2, 1, 2, 3, 5, 4, 9, 11, 11, 9, 8, 7, 8, 7, 7, 5, 5, 6, 3, 5, 4, 3, 2, 1, 3, 5, 5, 6, 7, 8, 11, 7, 14, 15, 14, 11, 9, 4, 9, 11
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
Let W denote the array of all positive rational numbers defined at A243712. For the present array, put (row 1) = (1), (row 2) = (-1, 3), (row 3) = (-1/2,0,3), and (row 4) = (-1/3,1/2,4). Thereafter, (row n) consists of the following numbers in increasing order: (row n) of W together -1/x for each x in (row n-1) of W.
|
|
LINKS
|
|
|
EXAMPLE
|
First 6 rows of the array of all positive rationals:
1/1
-1/1 ... 2/1
-1/2 ... 0/1 ... 3/1
-1/3 ... 1/2 ... 4/1
-2/1 .... -1/4 ... 2/3 ... 3/2 ... 5/1
-3/2 ... -2/3 ... -1/5 ... 3/4 ... 5/3 ... 5/2 ... 6/1
The denominators, by rows: 1,1,1,2,1,1,3,2,1,1,4,3,2,1,2,3,5,4,3,2,1,...
|
|
MATHEMATICA
|
z = 13; g[1] = {1}; f1[x_] := x + 1; f2[x_] := -1/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}]; u1 = Delete[Flatten[u], 10]
w[1] = 0; w[2] = 1; w[3] = 1; w[n_] := w[n - 1] + w[n - 3];
u2 = Table[Drop[g[n], w[n]], {n, 1, z}];
u3 = Delete[Delete[Flatten[Map[Reverse, u2]], 4], 4]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,tabf,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|