Harper's Sieve of Collatz

Abstract

Abstract This paper presents an algorithmic and programmatic optimization to the verification process of the Collatz Conjecture. A sieve is developed capable of a deterministic, monotonic reduction of the search space $\mathbb{N}$ via strict adherence to dyadic scaling of values and the subsequent parity vectors of their lower $k$ bits generating contractive affine transformations. The supporting data structure naturally encodes the commonly used $2^{k}$ modulo sieve and provides a new lens to view the classifications.