Post History

Collatz conjecture; Count the tries to reach $1$ [released]

# 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

$3x + 1$; Count the tries to reach $1$

# Background

Check out [this video on $3x + 1$](https://www.youtube.com/watch?v=094y1Z2wpJg).

If you know what this is, we're given an equation of $3x + 1$, and it is applied this way in the video:

- 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 $3x + 1$ problem:

- 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  → 6  (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  → 18 (9 → 28 → 14 → 7 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1)
10 → 7  (10 → 5 → 16 → 8 → 4 → 2 → 1)
```