Some Observations on the 3x+1 Problem

Abstract

We present some interesting observations on the 3x+1 problem. We propose a new algorithm which eliminates certain steps while we check the action of 3x+1 procedure on a number. Also, we propose a reason why many numbers follow a similar pattern during execution of 3x+1 algorithm. We advocate towards the end (a heuristic argument) that the 3x+1 conjecture is more likely to be true than false.