TITLE:
Collatz Sequences and Characteristic Zero-One Strings: Progress on the 3x + 1 Problem
AUTHORS:
David C. Kay
KEYWORDS:
Generator, Resultant, 3x + 1 Cycle
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.11 No.3,
September
30,
2021
ABSTRACT: The unsolved number theory problem known as the 3x + 1 problem involves
sequences of positive integers generated more or less at random that seem to
always converge to 1. Here the connection between the first integer (n) and the last (m) of a 3x + 1 sequence is analyzed by
means of characteristic zero-one strings. This method is used to achieve some
progress on the 3x + 1 problem. In particular, the long-standing conjecture that nontrivial cycles do not exist is virtually
proved using probability theory.