English

Look, Knave

Combinatorics 2021-07-01 v2

Abstract

We examine a recursive sequence in which sns_n is a literal description of what the binary expansion of the previous term sn1s_{n-1} is not. By adapting a technique of Conway, we determine limiting behaviour of {sn}\{s_n\} and dynamics of a related self-map of 2N2^{\mathbb{N}}. 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.

Keywords

Cite

@article{arxiv.2004.06414,
  title  = {Look, Knave},
  author = {Thomas Morrill},
  journal= {arXiv preprint arXiv:2004.06414},
  year   = {2021}
}
R2 v1 2026-06-23T14:50:32.870Z