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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A243854 Irregular triangular array of denominators of the positive rational numbers ordered as in Comments. 4
1, 1, 1, 1, 1, 1, 3, 5, 1, 3, 5, 3, 1, 3, 5, 9, 7, 3, 7, 1, 3, 5, 9, 7, 3, 5, 7, 7, 5, 2, 1, 3, 5, 9, 7, 3, 5, 7, 11, 7, 5, 2, 19, 29, 19, 13, 9, 1, 3, 5, 9, 7, 3, 5, 7, 11, 7, 5, 2, 19, 29, 19, 13, 11, 17, 9, 9, 17, 11, 13, 19, 6, 4, 5, 1, 3, 5, 9, 7, 3, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Decree that (row 1) = (1).  For n >= 2, row n consists of numbers in decreasing order generated as follows:  x+1 for each x in row n-1 together with 4/x for each x in row n-1, and duplicates are rejected as they occur.  Every positive rational number occurs exactly once in the resulting array.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..3000

EXAMPLE

First 6 rows of the array of rationals:

1/1

4/1 ... 2/1

5/1 ... 3/1

6/1 ... 4/3 ... 4/5

7/1 ... 7/3 ... 9/5 ... 2/3

8/1 ... 10/3 ... 14/5 .. 20/9 .. 12/7 .. 5/3 .. 4/7

The denominators, by rows:  1,1,1,1,1,1,3,5,1,3,5,3,1,3,5,9,7,3,7.

MATHEMATICA

z = 12; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 4/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[Reverse[g[n]], {n, 1, z}]; v = Flatten[u];

Denominator[v] (* A243854 *)

Numerator[v]   (* A243855 *)

Table[Length[g[n]], {n, 1, z}] (* A243856 *)

CROSSREFS

Cf. A243855, A243856, A242488, A243848.

Sequence in context: A231186 A021078 A130793 * A084243 A275056 A248916

Adjacent sequences:  A243851 A243852 A243853 * A243855 A243856 A243857

KEYWORD

nonn,easy,tabf,frac

AUTHOR

Clark Kimberling, Jun 12 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 January 18 07:12 EST 2019. Contains 319269 sequences. (Running on oeis4.)