A241837 Irregular triangular array of denominators of the positive rational numbers ordered as in Comments.

1, 1, 1, 1, 1, 1, 1, 1, 7, 5, 1, 1, 1, 1, 1, 4, 11, 5, 3, 2, 7, 5, 1, 1, 1, 1, 5, 5, 7, 13, 8, 10, 4, 11, 5, 3, 2, 7, 5, 1, 1, 1, 1, 2, 19, 3, 17, 13, 17, 11, 4, 13, 14, 19, 5, 5, 7, 13, 8, 10, 4, 11, 5, 3, 2, 7, 5, 1, 1, 1, 1, 7, 23, 11, 7, 6, 8, 19, 7, 23

Offset

1,9

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 n-1 together with 12/x for each nonzero x in row n-1, 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(n-1) 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 denominators, by rows:  1,1,1,1,1,2,1,1,7,5,1,1,1,1,1,4,11,5,3,2,7,5,1,1,1,1.

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. A243575, A243924, A022095.

Sequence in context: A350544 A256846 A336698 * A145176 A093205 A156536

Adjacent sequences: A241834 A241835 A241836 * A241838 A241839 A241840

Keyword

nonn,easy,tabf,frac

Author

Clark Kimberling, Jun 15 2014

Status

approved