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A132283 Normalization of dense fractal sequence A054065 (defined from fractional parts {n*tau}, where tau = golden ratio). 1
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; text; internal format)
OFFSET

1,3

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.)

REFERENCES

C. Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.

LINKS

Table of n, a(n) for n=1..98.

Clark Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, unpublished manuscript, 2007, cached copy, with permission.

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.

CROSSREFS

Cf. A132284.

Sequence in context: A194838 A085014 A082074 * A307081 A256440 A088370

Adjacent sequences:  A132280 A132281 A132282 * A132284 A132285 A132286

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 16 2007

STATUS

approved

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Last modified November 22 16:13 EST 2019. Contains 329396 sequences. (Running on oeis4.)