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A191544
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Dispersion of (floor(7n/3)), by antidiagonals.
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1
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1, 2, 3, 4, 7, 5, 9, 16, 11, 6, 21, 37, 25, 14, 8, 49, 86, 58, 32, 18, 10, 114, 200, 135, 74, 42, 23, 12, 266, 466, 315, 172, 98, 53, 28, 13, 620, 1087, 735, 401, 228, 123, 65, 30, 15, 1446, 2536, 1715, 935, 532, 287, 151, 70, 35, 17, 3374, 5917, 4001, 2181
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OFFSET
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1,2
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COMMENTS
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Background discussion: Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1. The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n)), s(s(s(t(n)))), ...). Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers. The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence. Examples:
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LINKS
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EXAMPLE
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Northwest corner:
1...2....4....9...21
3...7....16...37..86
5...11...25...58..135
6...14...32...74..172
8...18...42...98..228
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MATHEMATICA
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(* Program generates the dispersion array T of the complement of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12; f[n_] :=Floor[7n/3]] (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191544 sequence *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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