The Collatz Conjecture, also known as the 3n+1 Conjecture or the Ulam Conjecture, is an unsolved mathematical problem that was first proposed by the German mathematician Lothar Collatz in 1937. The conjecture is defined as follows:
Start with any positive integer n. If n is even, divide it by 2. If n is odd, multiply it by 3 and add 1. Repeat the process indefinitely for the resulting values, creating a sequence.
The conjecture states that no matter what positive integer you start with, the sequence will always eventually reach the value 1. Once the sequence reaches 1, it will enter an infinite loop: 1, 4, 2, 1, 4, 2, 1, and so on.
The significance of the Collatz Conjecture lies in its simplicity and the difficulty in proving or disproving it. Despite being easy to understand and verify for individual numbers, no counterexamples have been found, and the conjecture has been tested for extremely large numbers, making it one of the longest-standing unsolved problems in mathematics.
The Collatz Conjecture has attracted the interest of mathematicians for decades due to its elusive nature and the potential insights it could provide into the behavior of number sequences. It has connections to various areas of mathematics, such as number theory, dynamical systems, and graph theory. Solving the Collatz Conjecture would contribute to a deeper understanding of the properties and patterns of numbers.
In addition to being known as the Collatz Conjecture, it is also referred to as the 3n+1 problem or the Ulam Conjecture, named after the Polish mathematician Stanisław Ulam, who extensively studied and popularized the problem in the 20th century. A calculator notebook for Collatz Conjecture or commonly known as 3x+1 problem.
This repository is the implementation of Collatz Conjecture in Jupyter Lab. Try it on your computer or in Google Colab to visualize the prblem for any given positive integer, number of iterations, and all the intermediate numbers till you get stuck on the 4 2 1 loop.
https://colab.research.google.com/drive/1Wbo7ETbyHHG7DyzM9QZ56B8w_2_wUS5-?usp=sharing