Look, Knave

Authors

Keywords:

Recursion, Look-Say Sequence, Knights and Knaves

Abstract

We examine a recursive sequence in which s_n is a literal description of what the binary expansion of the previous term s_{n−1} is not. By adapting a technique of Conway, we determine limiting behaviour of {s_n} and dynamics of a related self-map of 2^{NN}. Our main result is the existence and uniqueness of a pair of binary sequences, each the compliment-description of the other. We also take every opportunity to make puns.

Published

2021-03-10

Issue

Vol. 103 No. 2 (2021)

Section

Articles
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