The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A243855 Irregular triangular array of numerators of the positive rational numbers ordered as in Comments. 4
 1, 4, 2, 5, 3, 6, 4, 4, 7, 7, 9, 2, 8, 10, 14, 20, 12, 5, 4, 9, 13, 19, 29, 19, 8, 12, 11, 10, 6, 1, 10, 16, 24, 38, 26, 11, 17, 18, 28, 17, 11, 3, 28, 36, 20, 12, 4, 11, 19, 29, 47, 33, 14, 22, 25, 39, 24, 16, 5, 47, 65, 39, 25, 20, 28, 14, 13, 20, 12, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 numerators, by rows:  1,4,2,5,3,6,4,4,,7,7,9,2,8,10,14,20,12,5,4. 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. A243854, A243856, A242488, A243848. Sequence in context: A059833 A123152 A309567 * A267185 A065187 A185511 Adjacent sequences:  A243852 A243853 A243854 * A243856 A243857 A243858 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 December 1 11:38 EST 2021. Contains 349429 sequences. (Running on oeis4.)