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A241837 Irregular triangular array of denominators of the positive rational numbers ordered as in Comments. 3

%I

%S 1,1,1,1,1,1,1,1,7,5,1,1,1,1,1,4,11,5,3,2,7,5,1,1,1,1,5,5,7,13,8,10,4,

%T 11,5,3,2,7,5,1,1,1,1,2,19,3,17,13,17,11,4,13,14,19,5,5,7,13,8,10,4,

%U 11,5,3,2,7,5,1,1,1,1,7,23,11,7,6,8,19,7,23

%N Irregular triangular array of denominators of the positive rational numbers ordered as in Comments.

%C Decree that (row 1) = (1,2,3). For n >=2, row n consists of numbers in increasing order generated as follows: x+4 for each x in row n-1 together with 12/x for each nonzero x in row n-1, where duplicates are deleted as they occur. Every rational number occurs exactly once in the array. The number of numbers in row n is A022095(n-1) for n >= 4.

%H Clark Kimberling, <a href="/A241837/b241837.txt">Table of n, a(n) for n = 1..5000</a>

%e First 4 rows of the array of rationals:

%e 1/1 .. 2/1 ... 3/1

%e 4/1 .. 5/1 ... 6/2 . 7/1 . 12/1

%e 12/7 . 12/5 .. 8/1 . 9/1 . 10/1 . 11/1 . 16/1

%e 3/4 .. 12/11 . 6/5 . 4/3 . 3/2 .. 40/7 . 32/5 . 13/1 . 14/1 . 15/1 . 20/1

%e The denominators, by rows: 1,1,1,1,1,2,1,1,7,5,1,1,1,1,1,4,11,5,3,2,7,5,1,1,1,1.

%t z = 10; g[1] = {1, 2, 3}; f1[x_] := x + 4; f2[x_] := 12/x; h[1] = g[1];

%t b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]]]];

%t h[n_] := h[n] = Union[h[n - 1], g[n - 1]];

%t g[n_] := g[n] = Complement [b[n], Intersection[b[n], h[n]]]

%t u = Table[g[n], {n, 1, z}]

%t v = Flatten[u]

%t Denominator[v] (* A241837 *)

%t Numerator[v] (* A243575 *)

%Y Cf. A243575, A243924, A022095.

%K nonn,easy,tabf,frac

%O 1,9

%A _Clark Kimberling_, Jun 15 2014

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Last modified June 16 12:38 EDT 2019. Contains 324152 sequences. (Running on oeis4.)