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

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Background

Check out this video on the Collatz conjecture, 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 code-golf, 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 for the link!


  1. https://oeis.org/A006577 ↩︎

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3 comment threads

OEIS (1 comment)
Test cases (2 comments)
It's called the Collatz Conjecture (2 comments)