Number Theory


3n+1 Problem for a Number Which Never Land

Authors: BOUARFAOUI Saïd

In the present paper, we study the 3n+1 problem to know if there is a theoretical number such as the number never land on the cycle {4;2;1}and grows continually.We will specify the general formula such as the number of uneven steps (3��+1)and even steps (��/2)are equals.We want to know also the uneven number form 2^��+2^0 and its composition during ��uneven (3��+1)and even steps (��/2).The composition number 2��+20will be viewed in two ways :1. When the powers which compose the numbers are expanded. We will recognize the Pascal’s triangle.2. When the powers which compose the numbers are agglutinate. We will recognize (3^��) in base 2.

Comments: 8 Pages. Some studies on the 3n+1 problem

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Submission history

[v1] 2019-12-02 13:53:35

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