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A191453
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Dispersion of (2*floor(3n/2)), by antidiagonals.
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1
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1, 2, 3, 6, 8, 4, 18, 24, 12, 5, 54, 72, 36, 14, 7, 162, 216, 108, 42, 20, 9, 486, 648, 324, 126, 60, 26, 10, 1458, 1944, 972, 378, 180, 78, 30, 11, 4374, 5832, 2916, 1134, 540, 234, 90, 32, 13, 13122, 17496, 8748, 3402, 1620, 702, 270, 96, 38, 15, 39366
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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....6....18...54
3...8....24...72...216
4...12...36...108..324
5...14...42...126..378
7...20...60...180..540
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MATHEMATICA
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(* Program generates the dispersion array T of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12;
f[n_] :=2Floor[3n/2] (* 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}]] (* A191453 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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