The 3x+1 Problem: An Overview

The 3x+1 problem, which is often called the Collatz problem, concerns the behavior of this function under iteration, starting with a given positive integer n. 3x+1 Conjecture. Starting from any positive integer n, iterations of the function C(x) will eventually reach the number 1. Thereafter iterations will cycle, taking successive values 1, 4, 2, 1, .... This problem goes under many other names, including the Syracuse problem, Hasse’s algorithm, Kakutani’s problem and Ulam’s problem. A commonly used reformulation of the 3x+1 problem iterates a different function, the 3x+ 1 function, given by

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