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 A243852 Irregular triangular array of numerators of the positive rational numbers ordered as in Comments. 4
 1, 3, 2, 4, 3, 5, 5, 3, 6, 7, 7, 6, 3, 7, 9, 11, 11, 12, 8, 6, 1, 8, 11, 15, 16, 19, 13, 15, 13, 15, 12, 2, 3, 9, 13, 19, 21, 26, 18, 23, 20, 26, 23, 5, 21, 10, 15, 21, 15, 4, 6, 3, 10, 15, 23, 26, 33, 23, 31, 27, 37, 34, 8, 34, 17, 28, 40, 21, 31, 9, 17, 33 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 numerators, by rows:  1,3,2,4,3,5,5,3,6,7,7,6,3,7,9,11,11,12,8,6,1. 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. A243851, A243853, A242488. Sequence in context: A052938 A302391 A140114 * A025532 A195459 A133131 Adjacent sequences:  A243849 A243850 A243851 * A243853 A243854 A243855 KEYWORD nonn,easy,tabf,frac AUTHOR Clark Kimberling, Jun 12 2014 STATUS approved

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Last modified October 17 08:13 EDT 2019. Contains 328106 sequences. (Running on oeis4.)