What is the Collatz conjecture?

The Collatz conjecture states that no matter which positive integer you start with, repeatedly applying the rule (even → n/2, odd → 3n+1) will always eventually reach 1. It has never been proven or disproven.

What is a "hailstone sequence"?

The sequence is nicknamed "hailstone" because the values rise and fall erratically — like hailstones in a storm — before eventually descending to 1.

Is there a number that never reaches 1?

None has been found. The conjecture has been verified computationally for all integers up to at least 2^68, but a formal proof does not yet exist.

Which starting number has the most steps?

Among small numbers, 27 takes 111 steps and reaches a peak of 9,232 before falling to 1 — making it a classic example of the conjecture's surprising behavior.

Why does this tool have a limit?

For very large starting numbers the sequence can have thousands of steps. The tool caps input at 10,000,000 to keep results responsive in the browser.

Collatz Sequence Calculator

Enter a positive integer to see its full Collatz sequence, step count, and peak value.

Starting Number

Positive integer (1 – 10,000,000)

Quick examples

Enter a number and click Generate

The full Collatz sequence will appear here

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Summary

The Collatz Sequence Calculator applies the 3n+1 rule to any positive integer and traces every step until the value reaches 1. It displays the complete sequence, the total step count, and the highest value (peak) encountered along the way. The tool runs entirely in your browser with no server calls.

How it works

Enter any positive integer in the input field.
The tool applies the Collatz rule: if the number is even, divide by 2; if odd, multiply by 3 and add 1.
Each result becomes the next input until the value reaches 1.
The full sequence is displayed step-by-step with the total number of steps and the peak (maximum) value reached.

Use cases

Explore the unsolved Collatz conjecture for specific numbers.
Compare how many steps different numbers take to reach 1.
Find the peak value a sequence hits before descending to 1.
Visualize the hailstone behavior of integers for math class or research.
Test whether large numbers eventually reach 1 (they all do, so far).

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu