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Proposed in 1937, the Collatz conjecture has remained in the spotlight formathematicians and computer scientists alike due to its simple proposal, yetintractable proof. In this paper, we propose several novel theorems,corollaries, and algorithms that explore relationships and properties betweenthe natural numbers, their peak values, and the conjecture. These contributionsprimarily analyze the number of Collatz iterations it takes for a given integerto reach 1 or a number less than itself, or the relationship between a startingnumber and its peak value.

Novel Theorems and Algorithms Relating to the Collatz Conjecture