Collatz Conjecture Calculator
Explore the famous 3n+1 problem
How to Use This Calculator
Enter Starting Number
Input any positive integer (whole number greater than 0). Try famous numbers like 27 or 7.
Click Calculate
Press the "Calculate Sequence" button to see the Collatz sequence generated from your starting number.
Review Results
See the complete sequence, number of steps to reach 1, and the maximum value encountered.
Collatz Conjecture Rules
If n is even: n → n/2
If n is odd: n → 3n + 1
Example: Starting with 7
7 (odd) → 3×7+1 = 22
22 (even) → 22/2 = 11
11 (odd) → 3×11+1 = 34
34 (even) → 34/2 = 17
...continues until reaching 1
7 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
About Collatz Conjecture Calculator
The Collatz Conjecture (also known as the 3n+1 problem, Ulam conjecture, or Syracuse problem) is one of the most famous unsolved problems in mathematics. The conjecture states that starting from any positive integer, if you repeatedly apply the Collatz rules, you will always eventually reach 1.
The Rules
- If the number is even, divide it by 2
- If the number is odd, multiply it by 3 and add 1
- Repeat the process with the new number
- The conjecture claims all sequences eventually reach 1
Why It's Famous
- It's deceptively simple to state but incredibly difficult to prove
- Despite being tested for numbers up to 2⁶⁸, no counterexample has been found
- Mathematician Paul Erdős said: "Mathematics is not yet ready for such problems"
- It remains one of the most famous unsolved problems in mathematics
Interesting Examples
- 27: Takes 111 steps and reaches a maximum of 9,232
- 7: Takes 16 steps to reach 1
- 1: Already at 1, takes 0 steps
Frequently Asked Questions
Has the Collatz Conjecture been proven?
No, the Collatz Conjecture remains unproven. It has been verified for numbers up to 2⁶⁸, but no general proof exists.
What happens if I start with 1?
Starting with 1 means you're already at the target. The sequence is just [1] with 0 steps.
Can I use negative numbers?
The standard Collatz Conjecture applies only to positive integers. Negative numbers can create cycles that never reach 1.
What's the longest sequence for small numbers?
For numbers under 100, 27 produces one of the longest sequences, taking 111 steps to reach 1.
Why is it called the 3n+1 problem?
The name comes from the rule for odd numbers: multiply by 3 and add 1 (3n + 1). The "n" represents the current number.