The Order of Numbers and the Collatz Problem

Abstract

The algorithm of Collatz is also known the 3n+1 problem. It will be started with any uneven natural number (n). This number is to triple and add one. Then divide by two as often as possible, if the number is even. If the number is odd, use again the 3n+1 step. The conjecture of the Collatz problem is that these operations always reach 1, no matter which positive integer is chosen to start the algorithm. A view to an order of numbers gives an explanation for the dominance of degressive steps to reach 1. The idea to identify the order of numbers is developed from an interview of Dr. Peter Plichta where he spoke on his book “Das Primzahlenkreuz”.