Look, Knave

Abstract: In this lighthearted tribute to the late John Conway, we examine a recursive sequence in which $s_n$ is a binary string that describes what the previous term $s_{n-1}$ is not. By adapting Conway's approach on the Look-and-Say sequence, we determine limiting behaviour of $\{s_n\}$ and dynamics of a related self-map on the space of infinite binary sequences. Our main result is the existence and uniqueness of a pair of binary sequences, each the compliment-description of the other.

number theory

Audience: researchers in the topic

Number Theory Online Conference 2020