Explaining Collatz Conjecture

Summary: Collatz conjecture has remained an unsolved mathematical puzzle.  In this note, we propose a “solution” to the conjecture.  The approach involves transformation of Collatz sequence by combining sequential steps, which helps reveal the underlying mechanism responsible for the observed convergence to unity. 1. Problem Statement Collatz conjecture states that if a) one starts with a positive natural number; b) divides it by 2 if even; c) triples it and adds 1 if it is odd; d) repeats (b) and (c) on the number thus obtained and repeats this step multiple times; the number would eventually converge to 1, whereafter these operations would keep yielding 1,4,2,1,4,2… Therefore, “Collatz Function” f(N) may be defined as follows: f(N) = N/2, if N is an even number f(N) = (3N+1), if N is an odd number Thus, for a starting number, the resulting series would be as follows: 27-->82-->41-->124-->62-->31-->94-->47-->142-->71-->214-->107-->322-->...