What is the Collatz conjecture?

The Collatz conjecture states that starting from any positive integer and repeatedly applying the rule — halve if even, otherwise triple and add one — you will always eventually reach 1. It is unproven for all numbers but verified for vast ranges.

What is stopping time?

Stopping time is the number of steps it takes for the sequence to first reach 1. For example, starting at 6 gives 6, 3, 10, 5, 16, 8, 4, 2, 1 — that is 8 steps.

Why are these called hailstone numbers?

Because the values rise and fall erratically, like hailstones being carried up and down in a storm cloud, before finally falling to 1. Some starting numbers soar to surprisingly large peaks before descending.

Can the sequence ever loop without reaching 1?

No known positive starting value loops or diverges — every tested number reaches 1. The conjecture that this always happens remains unproven in general, which is why it is one of mathematics' famous open problems.

Collatz Sequence Generator

The Collatz sequence (the “3n+1 problem”) follows a deceptively simple rule yet produces wildly unpredictable paths before always — as far as anyone has ever checked — settling on 1. This tool generates the complete sequence for any starting integer and reports its key statistics.

How it works

From a starting value n, repeat until you reach 1:

if n is even:  n = n / 2
if n is odd:   n = 3 × n + 1

So n = 6 produces 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1. The number of steps to first reach 1 is the stopping time, and the largest value seen along the way is the peak. BigInt is used so that even sequences that spike into very large numbers stay exact.

Example and tips

27 is a famous example: it takes 111 steps and climbs all the way to 9232 before crashing back down to 1. Watch how even small starting numbers can have long, jagged trajectories — that erratic, hailstone-like behaviour is exactly what makes the unproven Collatz conjecture so intriguing.