Collatz Conjecture Calculator
Explore the famous 3n + 1 problem. Enter any positive integer and visualize its trajectory.
Options
Use (3n + 1) / 2 for odd numbers
Use log scale on the graph
Safety limit to prevent freezing
Steps
111
Transitions required to reach 1
Highest Peak
9,232
Maximum value reached
Odd Steps
41
36.9% of total
Even Steps
70
63.1% of total
Final Value
1
Converged ✓
Trajectory Graph
Step-by-Step Sequence
112 steps| Step | Value | Parity | Operation | Next Value |
|---|---|---|---|---|
| 0 | 27 | Odd | 3n + 1 = 3 × 27 + 1 | 82 |
| 1 | 82 | Even | n / 2 = 82 / 2 | 41 |
| 2 | 41 | Odd | 3n + 1 = 3 × 41 + 1 | 124 |
| 3 | 124 | Even | n / 2 = 124 / 2 | 62 |
| 4 | 62 | Even | n / 2 = 62 / 2 | 31 |
| 5 | 31 | Odd | 3n + 1 = 3 × 31 + 1 | 94 |
| 6 | 94 | Even | n / 2 = 94 / 2 | 47 |
| 7 | 47 | Odd | 3n + 1 = 3 × 47 + 1 | 142 |
| 8 | 142 | Even | n / 2 = 142 / 2 | 71 |
| 9 | 71 | Odd | 3n + 1 = 3 × 71 + 1 | 214 |
| 10 | 214 | Even | n / 2 = 214 / 2 | 107 |
| 11 | 107 | Odd | 3n + 1 = 3 × 107 + 1 | 322 |
| 12 | 322 | Even | n / 2 = 322 / 2 | 161 |
| 13 | 161 | Odd | 3n + 1 = 3 × 161 + 1 | 484 |
| 14 | 484 | Even | n / 2 = 484 / 2 | 242 |
Sequence Summary
- Start Number
- 27
- Steps
- 111
- Highest Peak
- 9,232
- Odd Steps
- 41 (36.9%)
- Even Steps
- 70 (63.1%)
- Average Value
- 905.71
- Sequence length
- 112
Steps = transitions to reach 1. This matches the records table definition. Sequence length (one more) is shown below.
Sequence End
The sequence reached 1.
It will now repeat: 4, 2, 1, 4, 2, 1…
About the Conjecture
The Collatz Conjecture (also called the 3n + 1 problem) states that for any positive integer n, repeated application of the rule:
- •If n is even, divide by 2.
- •If n is odd, multiply by 3 and add 1.
…will always eventually reach 1. Despite being simple to state, it remains unproven.
Learn more →Custom Conjecture Lab
Experiment with rule variants and see how sequences behave.
Changing the rules creates a different problem. There is no guarantee that it will reach 1 or behave like the classic Collatz sequence.
Presets
Billions Tested
The conjecture has been verified computationally for very large ranges of positive integers.
All systems operationalUnproven
No complete mathematical proof exists yet for all positive integers.
Simple to State
Easy to explain to anyone, yet incredibly difficult to prove for the general case.
Infinite Curiosity
A problem that continues to fascinate mathematicians and computational researchers worldwide.