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A132283
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Normalization of dense fractal sequence A054065 (defined from fractional parts {n*tau}, where tau = golden ratio).
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1
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1, 1, 2, 1, 3, 2, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 9, 1, 6, 3, 8, 5, 10, 2, 7, 4, 9, 1, 6, 11, 3, 8, 5, 10, 2, 7, 4, 9, 1, 6, 11, 3, 8, 5, 10, 2, 7, 12, 4, 9, 1, 6, 11, 3, 8, 13, 5, 10, 2, 7, 12, 4, 9, 1, 14, 6, 11, 3, 8, 13
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A fractal sequence, dense in the sense that if i,j are neighbors in a segment, then eventually i and j are separated by some k in all later segments. (Hence in the "limit", i,j are separated by infinitely many other numbers.)
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REFERENCES
| C. Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.
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EXAMPLE
| Start with A054065=(1,2,1,2,1,3,2,4,1,3,5,2,4,1,3,5,2,4,1,6,3,5,2,...)
Step 1. Append initial 1.
Step 2. Write segments: 1; 1,2; 1,2; 1,3,2,4; 1,3,5,2,4;...
Step 3. Delete repeated segments: 1; 1,2; 1,3,2,4; 1,3,5,2,4; ...
Step 4. Make segment #n have length n by allowing only newcomer, namely n, like this: 1; 1,2; 1,3,2; 1,3,2,4; 1,3,5,2,4; 1,6,3,5,2,4; ...
Step 5. Concatenate those segments.
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CROSSREFS
| Cf. A132284.
Sequence in context: A194838 A085014 A082074 * A088370 A113787 A115624
Adjacent sequences: A132280 A132281 A132282 * A132284 A132285 A132286
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Aug 16 2007
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