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A191451
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Dispersion of (3n-2), for n>=2, by antidiagonals.
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4
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1, 4, 2, 13, 7, 3, 40, 22, 10, 5, 121, 67, 31, 16, 6, 364, 202, 94, 49, 19, 8, 1093, 607, 283, 148, 58, 25, 9, 3280, 1822, 850, 445, 175, 76, 28, 11, 9841, 5467, 2551, 1336, 526, 229, 85, 34, 12, 29524, 16402, 7654, 4009, 1579, 688, 256, 103, 37, 14, 88573
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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....13...40...121
2...7....22...67...202
3...10...31...94...283
5...16...49...148..445
6...19...58...175..526
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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_] :=3n+1 (* 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}]] (* A191451 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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