Collatz conjecture calculator
Enter any positive integer to trace its Collatz sequence. If even → divide by 2. If odd → multiply by 3 and add 1. Does it always reach 1?
The Collatz conjecture
Start with any positive integer n. If even, divide by 2. If odd, multiply by 3 and add 1. Repeat. The conjecture states that every starting number eventually reaches 1.
Why 27 is famous
Starting from 27 takes 111 steps and reaches a peak of 9,232 before finally descending to 1. It's a surprisingly long journey for such a small number.
Is it proven?
No. Despite being verified for all numbers up to 2⁶⁸ (about 2.95 × 10²⁰), no one has proven the conjecture. Mathematician Paul Erdős said "mathematics is not yet ready for such problems."
Interesting patterns
Powers of 2 reach 1 immediately (just divide repeatedly). Numbers of the form 2^k − 1 tend to have long sequences. The record holder under 10 billion is 9,780,657,630 with 1,132 steps.