# Background
Check out [this video on the Collatz conjecture](https://www.youtube.com/watch?v=094y1Z2wpJg), also known as A006577[^1].
If you don't know what this is, we're given an equation of $3x + 1$, and it is applied this way:
- If $x$ is odd, then $3x + 1$.
- If $x$ is even, then $\frac{x}{2}$.
This will send us in a loop of `4 → 2 → 1 → 4 → 2 → 1...`, which got me into making this challenge.
# Challenge
Write a program that establishes the Collatz conjecture:
- Take input of a positive integer. This will be the $x$ of the problem.
- Read the background for how it works, or watch the video for further explanation.
- The result should be how many turns it would take before reaching $1$. There, the sequence stops.
- This is <a class="badge is-tag">code-golf</a>, so the shortest program in each language wins!
# Test Cases
From 1 to 10:
```
1 → 0 (1)
2 → 1 (2 → 1)
3 → 7 (3 → 10 → 5 → 16 → 8 → 4 → 2 → 1)
4 → 2 (4 → 2 → 1)
5 → 5 (5 → 16 → 8 → 4 → 2 → 1)
6 → 8 (6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1)
7 → 16 (7 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1)
8 → 3 (8 → 4 → 2 → 1)
9 → 19 (9 → 28 → 14 → 7 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1)
10 → 6 (10 → 5 → 16 → 8 → 4 → 2 → 1)
```
More of these can be found on OEIS (see reference 1). Thanks to [**@Shaggy**](https://codegolf.codidact.com/users/53588) for the link!
[^1]: https://oeis.org/A006577
