Collatz Conjecture Calculator
Explore the Collatz sequence (3n+1 problem) and analyze convergence patterns
About this calculator
The Collatz Conjecture Calculator explores one of mathematics' most fascinating unsolved problems by generating the complete Collatz sequence for any positive integer. Also known as the 3n+1 problem, this calculator applies the simple rules: if the number is even, divide by 2; if odd, multiply by 3 and add 1. It visualizes the sequence's journey to 1, analyzes convergence patterns, and helps users understand this intriguing mathematical phenomenon that has captivated researchers for decades.
How to use
Enter any positive integer into the calculator and click calculate to generate the complete Collatz sequence. The tool will display each step of the sequence, showing how numbers transform according to the 3n+1 rules until reaching 1. Review the sequence length, maximum value reached, and convergence pattern to analyze the mathematical behavior.
Frequently asked questions
What is the Collatz Conjecture?
The Collatz Conjecture states that every positive integer will eventually reach 1 when following the 3n+1 sequence rules, though this remains unproven mathematically.
Why is it called the 3n+1 problem?
It's named after the rule: multiply odd numbers by 3 and add 1. Even numbers are simply divided by 2 until the sequence reaches 1.
Has the Collatz Conjecture been proven?
No, despite extensive computer verification for numbers up to very large values, no mathematical proof exists for all positive integers.