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 intriguing unsolved problems, also known as the 3n+1 problem. This tool generates and analyzes Collatz sequences for any positive integer, showing the step-by-step progression as numbers follow the simple rule: if even, divide by 2; if odd, multiply by 3 and add 1. It helps visualize convergence patterns, sequence lengths, and peak values, making this famous mathematical conjecture accessible for students, educators, and curious minds exploring number theory.
How to use
Enter any positive integer into the calculator and click generate. The tool will display the complete Collatz sequence, showing each step until reaching 1. You can analyze the total number of steps, highest value reached, and visualize the convergence pattern through the generated sequence data.
Frequently asked questions
What is the Collatz Conjecture?
The Collatz Conjecture states that every positive integer eventually reaches 1 when following the 3n+1 rule, though this remains mathematically unproven.
Are there any numbers that don't reach 1?
No counterexamples have been found despite extensive testing, but the conjecture remains unproven for all positive integers mathematically.
What's the longest Collatz sequence for small numbers?
The number 27 has one of the longest sequences under 100, taking 111 steps and reaching a peak of 9,232.