Collatz

[Alkatran]

I've been working with the Collatz series and noticed a pattern in the lengths. If you take the first occurence of a length, then find the first occurence of the next higher length after that, and continue... the steps will always be twice as large.

For example, from length 1 to length 2, the step is 1. From length 2 to length 3 the step is 2, and etc

I was just wondering what other patterns are known about it?

I'm current checking if the actual step in steps from length value to length value have some pattern...

[Alkatran]

Ah, the steps increase linearly. This only stands for the first occurence of numbers, but the next value is always n higher, where n is the position of the length.

It's been shown that if you can show the value mod 2 = 0, that it MUST go to 1, right? (assuming that it is true, but not proven yet)
Since it divides to become a smaller number, and all numbers lower than the test number are proven... right?
(this wouldn't apply to numbers other than the initial value)

[Alkatran]

How would I prove:


n is odd and greater than 4
2^x > n, 2^(x-1) < n
x is greater than 2 (as a consequence)

(n*3 + 1) mod (2^x) = (n mod (2^x)) - 1

[Gokul43201]

This doesn't look right...

n=5, x=3

(15+1) mod 8 = 0 but (5 mod 8) - 1 = 4

But then I don't know anything about the Collatz Sequence (other than that Comp Geeks find it fun and it has something to do with numbers of the form 3n+1).

[Alkatran]

This doesn't look right...

n=5, x=3

(15+1) mod 8 = 0 but (5 mod 8) - 1 = 4

But then I don't know anything about the Collatz Sequence (other than that Comp Geeks find it fun and it has something to do with numbers of the form 3n+1).

Change that -1 to a smaller than sign...

It was just one of those patterns you half see and need to check