This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A243851 Irregular triangular array of denominators of the positive rational numbers ordered as in Comments. 4
 1, 1, 1, 1, 2, 1, 2, 4, 1, 2, 4, 5, 5, 1, 2, 4, 5, 7, 5, 7, 2, 1, 2, 4, 5, 7, 5, 8, 7, 11, 11, 3, 7, 1, 2, 4, 5, 7, 5, 8, 7, 11, 11, 3, 13, 7, 13, 19, 16, 5, 11, 8, 1, 2, 4, 5, 7, 5, 8, 7, 11, 11, 3, 13, 7, 13, 19, 10, 16, 5, 11, 23, 8, 26, 20, 23, 6, 26, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Decree that (row 1) = (1) and (row 2) = (3,2).  For n >= 4, row n consists of numbers in decreasing order generated as follows:  x+1 for each x in row n-1 together with 3/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 3/1 ... 2/1 4/1 ... 3/2 5/1 ... 5/2 ... 3/4 6/1 ... 7/2 ... 7/4 ... 6/5 ... 3/5 7/1 ... 9/2 ... 11/4 .. 11/5 .. 12/7 .. 8/5 .. 6/7 .. 1/2 The denominators, by rows:  1,1,1,1,2,1,2,4,1,2,4,5,5,1,2,4,5,7,5,7,2. MATHEMATICA z = 12; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 3/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] (* A243851 *) Numerator[v]   (* A243852 *) Table[Length[g[n]], {n, 1, z}] (* A243853 *) CROSSREFS Cf. A243852, A243853, A242488. Sequence in context: A253572 A141539 A327844 * A168266 A059250 A303696 Adjacent sequences:  A243848 A243849 A243850 * A243852 A243853 A243854 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.

Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)