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A243928 Irregular triangular array of denominators of the positive rational numbers ordered as in Comments. 5
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 4, 1, 2, 2, 1, 1, 1, 5, 5, 4, 2, 1, 1, 1, 7, 7, 5, 5, 4, 2, 1, 1, 2, 1, 5, 3, 8, 7, 7, 5, 5, 5, 4, 2, 1, 1, 1, 1, 2, 4, 4, 7, 5, 3, 11, 3, 11, 3, 8, 4, 7, 7, 5, 5, 5, 4, 2, 1, 1, 1, 1, 2, 5, 4, 4, 8, 11, 8, 3, 4, 7, 13, 13, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Decree that (row 1) = (1). For n >=2, row n consists of numbers in increasing order generated as follows: x+1 for each x in row n-1 together with -3/x for each nonzero x in row n-1, where duplicates are deleted as they occur. The number of numbers in row n is A243930(n). Conjecture: every rational number occurs exactly once in the array.
LINKS
EXAMPLE
First 7 rows of the array of rationals:
1/1
-3/1 .. 2/1
-2/1 .. -3/2 .. 3/1
-1/1 .. -1/2 .. 3/2 ... 4/1
-3/4 .. 0/1 ... 1/2 ... 5/2 .. 5/1 .. 6/1
-6/1 .. -6/5 .. -3/5 .. 1/4 .. 7/2 .. 7/1
-12/1 . -5/1 .. -6/7 .. -3/7 . -1/5 . 2/5 . 5/4 . 9/2 . 8/1
The denominators, by rows: 1,1,1,1,2,1,1,2,2,1,4,1,2,2,1,1,1,5,5,4,2,1,1,1,7,7,5,5,4,2,1.
MATHEMATICA
z = 13; 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[g[n], {n, 1, z}]
v = Delete[Flatten[u], 23]
Denominator[v] (* A243928 *)
Numerator[v] (* A243929 *)
CROSSREFS
Sequence in context: A187450 A187449 A102541 * A286363 A233573 A025828
KEYWORD
nonn,easy,tabf,frac
AUTHOR
Clark Kimberling, Jun 15 2014
STATUS
approved

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Last modified April 18 16:22 EDT 2024. Contains 371780 sequences. (Running on oeis4.)