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 A243714 Irregular triangular array of denominators of all rational numbers ordered as in Comments. 5
 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 3, 2, 1, 2, 3, 5, 4, 3, 2, 1, 3, 5, 5, 6, 3, 5, 4, 3, 2, 1, 1, 4, 7, 8, 7, 7, 5, 5, 6, 3, 5, 4, 3, 2, 1, 2, 3, 5, 4, 9, 11, 11, 9, 8, 7, 8, 7, 7, 5, 5, 6, 3, 5, 4, 3, 2, 1, 3, 5, 5, 6, 7, 8, 11, 7, 14, 15, 14, 11, 9, 4, 9, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Let W denote the array of all positive rational numbers defined at A243712. For the present array, put (row 1) = (1), (row 2) = (-1, 3), (row 3) = (-1/2,0,3), and (row 4) = (-1/3,1/2,4). Thereafter, (row n) consists of the following numbers in increasing order: (row n) of W together -1/x for each x in (row n-1) of W. LINKS Clark Kimberling, Table of n, a(n) for n = 1..2000 EXAMPLE First 6 rows of the array of all positive rationals: 1/1 -1/1 ... 2/1 -1/2 ... 0/1 ... 3/1 -1/3 ... 1/2 ... 4/1 -2/1 .... -1/4 ... 2/3 ... 3/2 ... 5/1 -3/2 ... -2/3 ... -1/5 ... 3/4 ... 5/3 ... 5/2 ... 6/1 The denominators, by rows: 1,1,1,2,1,1,3,2,1,1,4,3,2,1,2,3,5,4,3,2,1,... MATHEMATICA z = 13; g[1] = {1}; f1[x_] := x + 1; f2[x_] := -1/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}]; u1 = Delete[Flatten[u], 10] w[1] = 0; w[2] = 1; w[3] = 1; w[n_] := w[n - 1] + w[n - 3]; u2 = Table[Drop[g[n], w[n]], {n, 1, z}]; u3 = Delete[Delete[Flatten[Map[Reverse, u2]], 4], 4] Denominator[u3] (* A243712 *) Numerator[u3] (* A243713 *) Denominator[u1] (* A243714 *) Numerator[u1] (* A243715 *) CROSSREFS Cf. A243712, A243713, A243715, A000930, A226130, A243613. Sequence in context: A136575 A309898 A193592 * A343656 A278427 A077592 Adjacent sequences: A243711 A243712 A243713 * A243715 A243716 A243717 KEYWORD nonn,easy,tabf,frac AUTHOR Clark Kimberling, Jun 09 2014 STATUS approved

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Last modified February 24 05:49 EST 2024. Contains 370293 sequences. (Running on oeis4.)