Discover the sequence of numbers generated by the Collatz Conjecture for any given positive integer. This tool is ideal for math enthusiasts and students exploring number theory.
All calculations are based on the established operations of the Collatz Conjecture. Visit Wikipedia for more information.
If the number is even, divide it by two. If it is odd, multiply it by three and add one:
$n = \begin{cases} n/2, & \text{if } n \text{ is even} \\ 3n + 1, & \text{if } n \text{ is odd} \end{cases}$
Starting with the number 6, the sequence is: 6, 3, 10, 5, 16, 8, 4, 2, 1. Each step follows the formula until reaching 1.
The Collatz Conjecture is a famous unsolved problem in mathematics. It states that starting with any positive integer and applying a specific sequence of operations will eventually lead to the number 1.
Despite its simple rules, the conjecture has not been proven or disproven, making it a significant topic of interest in mathematical research.
While the conjecture suggests the sequence will always reach 1, this has not been proven for all integers.
The conjecture is mainly of theoretical interest but provides a fascinating example of complexity arising from simple rules.
Use this calculator to input any positive integer and visualize the sequence it generates.