Construction of periods for 3x#x002B;1 problem: Use of division algorithm by 2 in 3-base number system for construction of 3-adic numbers as periods of collatz sequence

摘要

The division by 2 algorith for numbers written in 3-base number system is dicussed. This algorithm can be easily generalized to other odd base number systems. We used the algorithm for study of periods in sequence which appear in famous “3x+1 problem” or “Collatz problem”. The idea of using 3-adic numbers naturally arises from our discussion. We proved an interesting fact about the nature of periods in digits of these 3-adic numbers.