

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
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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 selfcontaining sequences, fractal sequences and parasequences, preprint, 2007.


LINKS

Table of n, a(n) for n=1..98.
Clark Kimberling, Proper selfcontaining sequences, fractal sequences and parasequences, unpublished manuscript, 2007, cached copy, with permission.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



