The Collatz conjecture says that this simple rule eventually reaches 1 from every positive starting number. It has been checked beyond 2⁶⁸ but never proved – Paul Erdős said “mathematics is not yet ready for such problems”.
How to use the Collatz Conjecture Calculator
- Starting number
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter a positive whole number. Exact big-integer arithmetic is used, so even huge numbers are followed correctly.
Formula
n → n/2 if n is even, n → 3n + 1 if n is odd
Worked example
Inputs — Starting number: 27.
Results — Steps to reach 1 = 111; Highest value reached = 9232; Sequence = 27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → 214 → 107 → 322 → 161 → 484 → 242 → 121 → 364 → 182 → 91 → 274 → 137 → 412 → 206 → 103 → 310 → 155 → 466 → 233 → 700 → 350 → 175 → 526 → 263 → 790 → 395 → 1186 → 593 → 1780 → 890 → 445 → 1336 → 668 → 334 → 167 → 502 → 251 → 754 → 377 → 1132 → 566 → 283 → 850 → 425 → 1276 → 638 → 319 → 958 → 479 → 1438 → 719 → 2158 → 1079 → 3238 → 1619 → 4858 → 2429 → 7288 → 3644 → 1822 → 911 → 2734 → 1367 → 4102 → 2051 → 6154 → 3077 → 9232 → 4616 → 2308 → 1154 → 577 → 1732 → 866 → 433 → 1300 → 650 → 325 → 976 → 488 → 244 → 122 → 61 → 184 → 92 → 46 → 23 → 70 → 35 → 106 → 53 → 160 → 80 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1.
Key terms
- Hailstone sequence
- Another name for a Collatz sequence.
Frequently asked questions
Has the Collatz conjecture been proved?
No – it remains open.
Why is 27 famous?
It takes 111 steps and climbs to 9,232 before falling to 1.
What is the stopping time?
The number of steps needed to reach 1.
Does every number reach 1?
Every number tested so far does.