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A241837 Irregular triangular array of denominators of the positive rational numbers ordered as in Comments. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A096435 A021855 A256846 * A145176 A093205 A156536

Adjacent sequences:  A241834 A241835 A241836 * A241838 A241839 A241840

KEYWORD

nonn,easy,tabf,frac

AUTHOR

Clark Kimberling, Jun 15 2014

STATUS

approved

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Last modified March 29 03:29 EDT 2017. Contains 284250 sequences.