Posted on 06/13/2023 3:38:58 PM PDT by Faith Presses On
I don’t have a mathematics background, but have done well in math generally, understand some of the concepts. I’ve been interested in this problem since seeing a YouTube video from the science channel Veritasium on the subject. After going over it for a time, I noticed some patterns in the numbers that are most divisible by 2. Here’s a summary of what I found, and I wonder how it fits into the picture.
1. Starting from 0: 3(0)+1=1.
2. Next, starting from 1: 3(1)+1=4. That’s the initial “4>2>1.”
3. Then, substitute 2: 3(2)+1=7. And 3: 3(3)+1=10. And 4: 3(4)+1=13.
4. Then, substituting 5: 3(5)+1=16. That’s 16>8>4>2>1.
5. 3(5)=15. 15+1=16. The 15/16 pair is likely highly important as it’s the first that reduces to the 4>2>1 loop.
6. Starting from 0: 3(0)+1=1.
– 1: 3(1)+1=4
– 2: 3(2)+1=7
– 3: 3(3)+1=10
There is a progression by 3, starting from 1: 1, 4, 7, 10, 13, 16…
7. Take those numbers, and plug them in here, as A: 5A+B. B simply starts at 0, and increases by 1 at every step (I chose A and B as I wasn’t a math major, as I said).
– 1(5)+0=5
– 4(5)+1=21
– 7(5)+2=37
– 10(5)+3=53
– 13(5)+4=69
– 16(5)+5=85.
The answer increases by 16 at every step.
8. Plug those answers as “x” into 3x+5:
– 3(5)+1=16
– 3(21)+1=64
– 3(37)+1=112
In the above, without adding the 1, the products are: 15, 63, and 111.
9. On the right side of the equation, the numbers are divisible by 16.
So you have:
– 3(5)+1=16(1)
– 3(21)+1=16(4)
– 3(37)+1=16(7)
https://www.youtube.com/watch?v=094y1Z2wpJg
“The Simplest Math Problem No One Can Solve - Collatz Conjecture”
- Veritasium
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What’s the question?
Don’t tell anyone, but I’m somewhat Math-Phobic.
I have artfully dodged being in a situation where I needed to utilize anything resembling a Slope. No one would ever know!
No! You're not the boss of me, alright!
42.
I’m with you.
It’s interesting. And you only have to divide even numbers.
First multiply any number by 3, then add 1. For instance, 3x5 is 15. Add 1, and it’s 16. Any time you get an even answer, keep dividing by 2. Every time the answer is odd (3x2+1=7), then multiply by 3 and add 1 again. Keep doing it. The numbers often get enormous. But eventually, all numbers, as far as they can tell, end up at 1. 4,2,1 at the end. But there’s no proof for it.
So take 3, for example. 3x3 plus 1 is 10. 10 can be divided by 2, so you get 5. But that has to be multiplied by 3, and then 1 added: 3x5 plus 1 is 16. And that gets you to 16 > 8> 4> 2> 1.
This is interesting even if you’re math phobic. You only have to divide if a number is even. And actually, there are sites that do all the calculations for you. The video I linked to explains it well.
You need a hobby.
(or a cat)
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