Collatz Conjecture Calculator

Math

Explore the Collatz conjecture: apply n → n/2 (if even) or n → 3n+1 (if odd) and count steps to reach 1.

Formula

n → n/2 if n is even; n → 3n+1 if n is odd; repeat until n = 1
  • The Collatz conjecture states that every positive integer eventually reaches 1.
  • The sequence is also called the hailstone sequence due to its up-and-down nature.
  • As of 2023, the conjecture has been verified for all numbers up to 2^68 but not proven in general.

Starting at 27

Inputs
  • Starting Number: 27

27 → 82 → 41 → 124 → ... reaches a peak of 9232 after 111 steps before descending to 1.

Frequently asked questions

What is the Collatz conjecture?
An unsolved mathematical conjecture that every positive integer, under the 3n+1 rule, eventually reaches 1.
Has it been proven?
No — it is one of the most famous unsolved problems in mathematics.
What is the longest sequence under 1000?
n=871 has 178 steps and reaches a peak of 190,996 before reaching 1.
Why is it called the hailstone sequence?
The values go up and down many times (like hailstones rising and falling in clouds) before ultimately reaching 1.