A243575 Irregular triangular array of numerators of the positive rational numbers ordered as in Comments.

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

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 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 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: A175500 A356253 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