Conway's subprime Fibonacci sequences
Number Theory
2016-01-06 v2 Combinatorics
Abstract
It's the age-old recurrence with a twist: sum the last two terms and if the result is composite, divide by its smallest prime divisor to get the next term (e.g., 0, 1, 1, 2, 3, 5, 4, 3, 7, ...). These sequences exhibit pseudo-random behaviour and generally terminate in a handful of cycles, properties reminiscent of 3x+1 and related sequences. We examine the elementary properties of these 'subprime' Fibonacci sequences.
Cite
@article{arxiv.1207.5099,
title = {Conway's subprime Fibonacci sequences},
author = {Richard K. Guy and Tanya Khovanova and Julian Salazar},
journal= {arXiv preprint arXiv:1207.5099},
year = {2016}
}
Comments
18 pages, 5 figures