Collatz congecture

Discussion
1

does anybody know how to make a collatz congecture in desmos?i get that its hard,but you could start using that method for checking the amount of something

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2

Here it is! Also, the most elements of a I have found was 9381. It gives 153 list elements.

Edit: 193819382893 gives 384 elements!

3

thank you very much!

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4

thank you! also 314159265358979300 gives 397

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5

Somehow 194859859344775784589433030489050358765 only gives 360

6

67 gets 27,which brings up the question of the max ratio of simulations:starting value
edit #1:27 takes 111 simulations
edit#2:1000011 takes 113,and is binary

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7

Challenge for you:

Could you make a function, say g(x), that returns the number of iterations that it would take to get x to the “repeat” (the 4, 2, 1 repeat) using the Collatz Conjecture?

8

I learned that 75128138247 takes 1228 iterations using Google

9

i dont know how to proform the len(x) function in desmos,sorry

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10

In the regular calculator you can use count(), .count, length() or .length. Either count is better to use because copying to or from the geometry calculator can end up with errors using length, which is for the measurement of segments in that calculator.

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No, I meant like you plug in any value and it knows how long the numbers list will be.

Edit: Just realized that this is basically impossible right now

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“No Known Pattern or Formula There’s no known way to predict how long a number will take to reach 1 (called its “total stopping time”) or how high it will go. This lack of structure makes the behavior seem random, even though it’s entirely deterministic.” (Credit: CopilotAI by Microsoft)

13

i mean,you could run it and then do the length

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14

I guess, but that wouldn’t really be an actual function.

15

yeah.i wish the graphing calculator had a bit of python

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16

it would be interesting if you graphed that relationship

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17

What relationship? The number of iterations to greatest number?

18

no,
n
(summation simbol (number of itterations starting with y))/|n-y|
y
i just learned summation. my life is worse after trying to use it in 7th grade class today

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19

\frac{\left(\sum_{n=d}^{z}\operatorname{length}\left(n_{umbers}\right)\right)}{\left|d-z\right|+1} is a example starter

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