The Collatz Conjecture

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Das Troll
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The Collatz Conjecture

Post by Das Troll » Tue Jun 30, 2020 1:27 pm

Are you smart? Think you're smarter than the worlds math geniuses? Try and figure this out.

Two rules to this game:

If even: n/2
If odd: 3n+1

n being any whole number. No matter what whole number you pick it will always end in 4, 2, and lastly 1.

Any 4th grader can do this math, but the trick is why it happens with any positive whole number.

More on the Collatz Conjecture

https://en.wikipedia.org/wiki/Collatz_conjecture

AngryIVer
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Re: The Collatz Conjecture

Post by AngryIVer » Tue Jun 30, 2020 7:58 pm

3n+1 being 3xn+1, right?
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Das Troll
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Re: The Collatz Conjecture

Post by Das Troll » Tue Jun 30, 2020 10:48 pm

AngryIVer wrote:
Tue Jun 30, 2020 7:58 pm
3n+1 being 3xn+1, right?
yes

Das Troll
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Re: The Collatz Conjecture

Post by Das Troll » Wed Jul 01, 2020 3:15 am

Little factoid:

The longest progression for any initial starting number less than 100 million is 63,728,127, which has 949 steps. For starting numbers less than 1 billion it is 670,617,279, with 986 steps, and for numbers less than 10 billion it is 9,780,657,630, with 1132 steps.

It gets extra weird when its represented in a picture.
collatz.png
collatz.png (74.95 KiB) Viewed 42 times
BTW you can shorten the equation a tad by 3x+1/2 since this part will always produce a even number.

AngryIVer
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Re: The Collatz Conjecture

Post by AngryIVer » Wed Jul 01, 2020 5:14 am

I had more time to look at the Wiki entry (I was curious why 1 didn't follow those rules) and noticed a lot of numbers ending in 0?
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Das Troll
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Re: The Collatz Conjecture

Post by Das Troll » Wed Jul 01, 2020 1:24 pm

AngryIVer wrote:
Wed Jul 01, 2020 5:14 am
I had more time to look at the Wiki entry (I was curious why 1 didn't follow those rules) and noticed a lot of numbers ending in 0?
Beats me. I don't know why it happens. I'm no genius.

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Re: The Collatz Conjecture

Post by AngryIVer » Wed Jul 01, 2020 5:50 pm

OHHHHH I get it now, actually. The idea is that using those two formulas you can start from a HIGH number and reach 1. The graph threw me off because I thought the sequence was counting UP when that's just the number of steps to hit 1 starting at increasingly higher numbers.
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