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A112382
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A self-descriptive fractal sequence: the sequence contains every positive integer. If the first occurrence of each integer is deleted from the sequence, the resulting sequence is the same is the original (this process may be called "upper trimming").
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3
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1, 1, 2, 1, 3, 4, 2, 5, 1, 6, 7, 8, 3, 9, 10, 11, 12, 4, 13, 14, 2, 15, 16, 17, 18, 19, 5, 20, 1, 21, 22, 23, 24, 25, 26, 6, 27, 28, 29, 30, 31, 32, 33, 7, 34, 35, 36, 37, 38, 39, 40, 41, 8, 42, 43, 44, 3, 45, 46, 47, 48, 49, 50, 51, 52, 53, 9, 54, 55, 56, 57, 58, 59, 60
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internal format)
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OFFSET
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0,3
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COMMENTS
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This sequence is also self-descriptive in that each element gives the number of first occurrences of integers (X's in the example) that were removed just before it.
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LINKS
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EXAMPLE
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If we denote the first occurrence of each integer by X we get:
X, 1, X, 1, X, X, 2, X, 1, X, X, X, 3, X, X, X, X, 4, X, X, 2, ...
and dropping the X's:
1, 1, 2, 1, 3, 4, 2, ...
which is the beginning of the original sequence.
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MATHEMATICA
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uppertrim[list_]:= Fold[DeleteCases[#1, #2, 1, 1]&, list, Range[Max[list]]]; Nest[Flatten[Append[#, Append[Range[Max[#] + 1, Max[#] + #[[Length[uppertrim[#]] + 1]]], #[[Length[uppertrim[#]] + 1]]]]] &, {1, 1}, 10] (* Birkas Gyorgy, Apr 27 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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