Math of how numbers are written

Lets make a sequence starting by spitting each digit of any number in half literally.

Next we create our next number in our sequence by counting up the number of segments before it.

The sequence keeps on repeating the number 4.

Other sequences:

0, 2, 4
123, 12, 7, 3, 5, 4

This reminds me how the word four has 4 letters

With this I have a few questions:

Does staring with any whole number always converge towards 4?
What if we write our numbers differently, what will these numbers converge to?
What's up with you, number 4?

#NumberTheory

Easy Math Editor

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Math	Appears as
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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

VERY INTERESTING

Michael Wang - 3 years ago

Thanks! It takes me a while to write down ideas and I appreciate feedback.

Brack harmon - 3 years ago

Of course you get get any result if you change the numbers :P But it is funny that they all go to 4, even if it is just coincidence. I assume any whole number will converge to 4, since 0,1,2,3,4,and 5 all converge. Otherwise that would imply there is some other equilibrium, and no number is going to split into >6 segments. If it's several digits then it still doesn't matter - it will decrease unless each digit splits into like 10+ different pieces

Alex Li - 3 years ago

How do you get 4 pieces out of four?

Blan Morrison - 3 years ago

I used the cambria font for this problem, and the letter 4 has a small yet noticeable horizontal line on the bottom which i counted. If you exclude the horizontal line you end up with a repetition of 4,2,4,2.

Brack harmon - 3 years ago

Ok, so that means there are two separate "games:" Serif and Sans-Serif.

Question: When you did 123, did you split each digit in half, or the entire number?

Also, there is a typo in your third paragraph. Don't worry, we all make mistakes.

Blan Morrison - 3 years ago

@Blan Morrison – To clarify, I spit each digit in half and added up all the segments of all the digits. Also, it's quite ironic I misspelled the word number.

Brack harmon - 3 years ago

I agree to that: If it's several digits then it still doesn't matter - it will decrease unless each digit splits into like 10+ different pieces

Marcel Probst - 3 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$