2Free Tetranacci Sequences
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 divisionpoor" 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 arXiv:
 arXiv:1710.00930
 Bibcode:
 2017arXiv171000930A
 Keywords:

 Mathematics  Number Theory;
 11B39