2024/01/25 by Éric Angelini, Michael S. Branicky, Angelini, Eric +7
Computer Science · #11B37 11B75 #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic, programming, and type systems #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2401.14346
openalex publication_date 2024/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The ``comma sequence'' starts with 1 and is defined by the property that if k and k' are consecutive terms, the two-digit number formed from the last digit of k and the first digit of k' is equal to the difference k'-k. If there is more than one such k', choose the smallest, but if there is no such k' the sequence terminates. The sequence begins 1, 12, 35, 94, 135, ... and, surprisingly, ends at term 2137453, which is 99999945. The paper analyzes the sequence and its generalizations to other starting values and other bases. A slight change in the rules allows infinitely long comma sequences to exist.