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A191452
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Dispersion of (4,8,12,16,...), by antidiagonals.
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9
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1, 4, 2, 16, 8, 3, 64, 32, 12, 5, 256, 128, 48, 20, 6, 1024, 512, 192, 80, 24, 7, 4096, 2048, 768, 320, 96, 28, 9, 16384, 8192, 3072, 1280, 384, 112, 36, 10, 65536, 32768, 12288, 5120, 1536, 448, 144, 40, 11, 262144, 131072, 49152, 20480, 6144, 1792, 576
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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...4....16....64...256
2...8....32...128...512
3...12...48...192...768
5...20...80...320...1280
6...24...96...384...1536
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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_] :=4n (* 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}]] (* A191452 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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