Date of Award
2010
Document Type
Thesis
Department
Mathematics
First Reader
Dr. Jeffrey Sykes
Second Reader
Dr. Steve Hennagin
Third Reader
Dr. Johnny Wink
Abstract
The 3n + l Conjecture states that when the Collatz function is applied repeatedly to an initial value, the sequence of values generated always converges to 1, regardless of the starting value. This paper strengthens the claim that all such sequences are convergent by showing that certain types of nonconvergent sequences cannot exist. Specifically, no sequence with parity-periodic values can exist This eliminates all possible nontrivially periodic sequences and all divergent sequences with periodic parity. Therefore, if a counterexample to the conjecture exists, It must be a divergent sequence whose values display no parity periodicity.
Recommended Citation
Phillips, Austin J., "Parity Periodicity: An Eliminative Approach to the Collatz Conjecture" (2010). Honors Theses. 53.
https://scholarlycommons.obu.edu/honors_theses/53