Look and Say Sequences

AUTHORS: Aspram Kharatyan and Santosh Acharya
FACULTY: Jonny Comes
DEPARTMENT: Mathematics and Physical Sciences

ABSTRACT

John Conway introduced the study of look and say sequences in 1986. By exploring look and say sequences with standard number system, Conway found a magic number (known as Conway's constant) that gives the growth rate for any standard look and say sequence and established a Cosmological Theorem that completely describes the structure of the sequence. In this project, we explored a variation of look and say sequences obtained by replacing the standard number system with a family of non-standard binary number systems with nth-root-2 as a binary base (where n is any integer, $n>1$). We determined growth rates for many of these sequences, and we proved Cosmological Lemma that allows us to describe the structure of all look and say sequences for any particular n.