Arithmetic Sequences and Blocks of Powers of Two in the Collatz Array

Abstract

In this short paper, we examine a curious feature of the Collatz function. When the sequences generated by the Collatz function on consecutive integer initial points are arranged into an array, certain arithmetic sequences show up with common differences given by products of twos and threes. The common differences themselves are further related by a formula that depends on even versus odd input. While we do not solve the Collatz Conjecture by this observation, we present our findings as interesting mathematical results in their own rights.