2-Free Tetranacci Sequences
Number Theory
2017-10-04 v1
Abstract
We consider a variant on the Tetranacci sequence, where one adds the previous four terms, then divides the sum by two until the result is odd. We give an algorithm for constructing "initially division-poor" sequences, where over an initial segment one divides by two only once for each term. We develop a probabilistic model that suggests that "most" sequences are unbounded, and provide computational data to support the underlying assumptions of the model.
Cite
@article{arxiv.1710.00930,
title = {2-Free Tetranacci Sequences},
author = {Jeremy F. Alm and Taylor Herald and Ellen Rammelkamp Miller and Dave Sexton},
journal= {arXiv preprint arXiv:1710.00930},
year = {2017}
}