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A167198
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Fractal sequence of the interspersion A083047.
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3
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1, 1, 2, 1, 2, 3, 1, 4, 2, 3, 5, 1, 4, 6, 2, 7, 3, 5, 8, 1, 9, 4, 6, 10, 2, 7, 11, 3, 12, 5, 8, 13, 1, 9, 14, 4, 15, 6, 10, 16, 2, 17, 7, 11, 18, 3, 12, 19, 5, 20, 8, 13, 21, 1, 22, 9, 14, 23, 4, 15, 24, 6, 25, 10, 16, 26, 2, 17, 27, 7, 28, 11, 18, 29, 3, 30, 12, 19, 31, 5, 20, 32, 8, 33, 13
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OFFSET
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1,3
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COMMENTS
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As a fractal sequence, if the first occurrence of each term is deleted, the remaining sequence is the original. In general, the interspersion of a fractal sequence is constructed by rows: row r consists of all n, such that a(n)=r; in particular, A083047 is constructed in this way from A167198.
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REFERENCES
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Clark Kimberling, Stolarsky interspersions, Ars Combinatoria 39 (1995), 129-138.
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LINKS
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FORMULA
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Following is a construction that avoids reference to A083047.
Write initial rows:
Row 1: .... 1
Row 2: .... 1
Row 3: .... 2..1
Row 4: .... 2..3..1
For n>=4, to form row n+1, let k be the least positive integer not yet used; write row n, and right before the first number that is also in row n-1, place k; right before the next number that is also in row n-1, place k+1, and continue. A167198 is the concatenation of the rows. (If "before" is replaced by "after", the resulting fractal sequence is A003603, and the associated interspersion is the Wythoff array, A035513.)
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EXAMPLE
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To produce row 5, first write row 4: 2,3,1, then place 4 right before 2, and then place 5 right before 1, getting 4,2,3,5,1.
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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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