login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A243575 Irregular triangular array of numerators of the positive rational numbers ordered as in Comments. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A178531 A175500 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 17:27 EDT 2019. Contains 324234 sequences. (Running on oeis4.)