Collatz Sequence Generator
Generate Collatz sequences (3n+1 problem) for any starting number with step tracking, max value analysis, and sequence visualization. Explore the famous unsolved conjecture with detailed hailstone sequence generation and statistical breakdowns.
Enter a positive integer between 1 and 10,000
Complete Guide: Collatz Sequence Generator
Everything you need to know about using this tool effectively
The Collatz Sequence Generator computes the 3n+1 sequence for any positive integer you enter. The Collatz conjecture states that repeating 'if even divide by 2, if odd multiply by 3 and add 1' always reaches 1. The tool shows every step, the total number of steps, and the peak value reached. All processing happens in the browser.
This tool applies the Collatz rules iteratively: if n is even, n = n / 2. If n is odd, n = 3n + 1. It repeats until n reaches 1, recording each value in the sequence. The output includes the full sequence, step count, and statistics.
Exploring the Collatz conjecture
Test different starting numbers to see how the sequence behaves.
Teaching iterative algorithms
Use as a classroom example of a simple algorithm with complex behavior.
Mathematical research
Analyze sequence lengths and peak values across ranges of starting numbers.
Programming exercises
Implement the Collatz sequence as a coding challenge and verify results.
Enter a starting number
Type any positive integer.
Generate the sequence
Click Generate. The tool computes every step.
Review the results
See the full sequence, step count, and peak value.
Copy or download
Copy the sequence or download it.
The Collatz conjecture has been tested up to 2^68 but remains unproven.
Larger starting numbers generally produce longer sequences.
The peak value is often much larger than the starting number.
1 is the trivial case: the sequence is just [1].
What is the Collatz conjecture?
The Collatz conjecture states that for any positive integer, repeatedly applying 'if even, divide by 2; if odd, multiply by 3 and add 1' will eventually reach 1. It has been verified for extremely large numbers but remains unproven.
What does the tool show?
The full sequence of numbers, the total number of steps to reach 1, and the peak (maximum) value encountered.
Is my data sent to a server?
No. All computation happens in your browser. Nothing is transmitted.
Can I use very large numbers?
Yes. The tool handles large integers. Very large numbers may produce very long sequences that take time to compute.
Why is it called 3n+1?
The odd step (3n + 1) gives the sequence its alternative name. The sequence is also called the hailstone sequence because values rise and fall like hailstones in a cloud.