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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 Table of n, a(n) for n=1..38. 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 Cf. A243925, A243926, A243930. Sequence in context: A055501 A096010 A241507 * A102330 A103598 A103403 Adjacent sequences: A243924 A243925 A243926 * A243928 A243929 A243930 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.)