On the Lattice of 2^n -1 in the Collatz Conjecture

EasyChair Preprint 5322, version 4

Abstract

The elements of 2^n − 1 when arranged in ascending order of n, n ∈ N
form a fine lattice with respect to some diagonal. The focus of this paper
is on the leading diagonal in the pursuit of reducing the calculational
complexity. One such short cut will focus on the summands of the powers
of 3. The finding is the sum
exhibits a Collatz like behavior. Armed
with that we can reduce the amount of cycles considerably.

Keyphrases: 3k + 1, Collatz Conjecture, chaos theory

@booklet{EasyChair:5322,
  author    = {Alex Nguhi},
  title     = {On the Lattice of 2^n -1 in the Collatz Conjecture},
  howpublished = {EasyChair Preprint 5322},
  year      = {EasyChair, 2022}}