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Comments on Collatz conjecture; Count the tries to reach 1

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Collatz conjecture; Count the tries to reach 1

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Background

Check out this video on the Collatz conjecture, also known as A006577.

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 x2.

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. Thanks to @Shaggy for the link!

code-golf math number
posted over 3 years ago
3y ago by celtschk‭
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General Sebast1an‭
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Wolfram Language (Mathematica), 38 bytes

Tr[1^ResourceFunction["Collatz"]@#]-1&

Don't Try it online!

Doesn't work on TIO due to using the Collatz builtin which needs to be downloaded from the Function Repository

Relatively badly-golfed version without ResourceFunction (52 bytes):

i=0;If[#!=1,i++;#0[If[EvenQ@#,Floor[#/2],3 #+1]],i]&

Try it online!

Had to add a slightly janky print statement into the main body for the value of i to get reset on each evaluation.

posted about 3 years ago
3y ago
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romanp‭
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1 comment thread

Saving 9 characters in the version without Collatz builtin (1 comment)
Saving 9 characters in the version without Collatz builtin
celtschk‭ wrote about 3 years ago
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You don't need the Floor here. When dividing an even integer by 2, Mathematica automatically gives an integer. Also, the space in 3 # is unnecessary. And #!=1 can be replaced by #>1.