#### Title

#### Document Type

Article

#### Publication Date

1-2010

#### Abstract

Define the Linus sequence *L _{n}* for

*n*≥ 1 as a 0–1 sequence with

*L*

_{1}= 0, and

*L*chosen so as to minimize the length of the longest immediately repeated block

_{n}*L*

_{n−2r+1}

*L*=

_{n−r}*L*

_{n−r+1}

*L*. Define the Sally sequence

_{n}*S*as the length

_{n}*r*of the longest repeated block that was avoided by the choice of

*L*. We prove several results about these sequences, such as exponential decay of the frequency of highly periodic subwords of the Linus sequence, zero entropy of any stationary process obtained as a limit of word frequencies in the Linus sequence and infinite average value of the Sally sequence. In addition we make a number of conjectures about both sequences.

_{n}#### Publication Title

Combinatorics Probability & Computing

#### Volume

19

#### Issue

1

#### First Page

21

#### Last Page

46

#### Required Publisher's Statement

Copyright 2010 Cambridge University Press. The original published version of this article may be found at http://dx.doi.org/10.1017/S0963548309990198.

#### Recommended Citation

Balister, Paul; Kalikow, Steve; and Sarkar, Amites, "The Linus Sequence" (2010). *Mathematics.* Paper 4.

http://cedar.wwu.edu/math_facpubs/4