Collatz conjecture
Unproved: starting from any positive integer, repeating the rule always reaches 1. History: 1937.
How to work it out
- 1
The statement:
- 2
Unproved: starting from any positive integer, repeating the rule always reaches 1.
- 3
Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ n \mapsto \begin{cases} n/2 & n \text{ even} \\ 3n+1 & n \text{ odd} \end{cases} \]Steps to reach 1 (computed)
| Start | Steps | Highest value reached |
|---|---|---|
| 6 | 8 | 16 |
| 7 | 16 | 52 |
| 9 | 19 | 52 |
| 12 | 9 | 16 |
| 19 | 20 | 88 |
| 27 | 111 | 9232 |
| 97 | 118 | 9232 |
Questions
What is the collatz conjecture?
Unproved: starting from any positive integer, repeating the rule always reaches 1.
Who is the Collatz conjecture associated with?
Paul Erdős.