## DIMACS TR: 93-84

## Notes on the Kolakoski Sequence

### Author: Vasek Chvatal

**
ABSTRACT
**

The Kolakoski sequence,
12211212212211211221211212211211212212211212212112..., is the unique
countable 1-2 sequence a_1a_2a_3... with a_1=1, whose j-th block has
length a_j; Keane asked whether the density of 1's (and therefore also
the density of 2's) in this sequence is 0.5. The purpose of this note
is twofold: (i) to report computations proving that the upper density
of 1's as well as the upper density of 2' in the Kolakoski sequence is
less than 0.501, and (ii) to speculate about possible ways of
answering Keane's question in the affirmative.

Paper available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1993/93-84.ps

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