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A243927 Number of numbers in row n of the array at A243925. 5
1, 2, 2, 3, 3, 5, 8, 11, 13, 19, 28, 42, 60, 88, 123, 176, 252, 371, 531, 768, 1091, 1581, 2256, 3262, 4685, 6818, 9755, 14167, 20321, 29465, 42275, 61280, 88082, 127736, 183613, 266012, 382840, 554373 (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 increasing order generated as follows: x+1 for each x in row n-1 together with -2/x for each nonzero x in row n-1, where duplicates are deleted as they occur. The number of numbers in row n is A243927(n). Conjecture: every rational number occurs exactly once in the array.
LINKS
EXAMPLE
First 7 rows of the array of rationals:
1/1
-2/1 ... 2/1
-1/1 ... 3/1
-2/3 ... 0/1 ... 4/1
-1/2 ... 1/3 ... 5/1
-6/1 ... -2/5 .. 1/2 ... 4/3 ... 6/1
-5/1 ... -4/1 .. -3/2 .. -1/3 .. 3/5 .. 3/2 .. 7/3 .. 7/1, so that the first 7 terms of A243927 are 1,2,2,3,3,5,8.
MATHEMATICA
z = 20; g[1] = {1}; f1[x_] := x + 1; f2[x_] := -2/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]]]; g[5] = Delete[g[5], 4]; Table[Length[g[n]], {n, 1, z}] (* A243927 *)
CROSSREFS
Sequence in context: A055501 A096010 A241507 * A102330 A103598 A103403
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 15 2014
STATUS
approved

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Last modified April 18 15:05 EDT 2024. Contains 371780 sequences. (Running on oeis4.)