Hello world, how is it going?

Collatz Conjecture, ever heard of it? It’s probably most known as “3n+1” or “Half Or Triple Plus One” .

The procedure is pretty simple and starts with a simple *number picking*. So yes, pick any number, let’s call this number **n**.

algorithm: (<– : stands for assignment)

- if your number n is odd then do the following instruction:
** new_n <– n * 3 + 1**;** n<– new_n;**
- if your number n is even, then divise it by two:
**new_n <– n/2; n<– new_n;**
- Repeat the algorithm until you get your number
**n**‘1’

Now you see, you’re always going to converge and get “1” at the end or to be more exact “**4-2-1**” sequence. And that would be with any number you take!

Well, that’s nice, but I have other words to say about these.

As the goal of the algorithm is to make 1.5*n converges, then 3N+1 wouldn’t be the only maze in here!

5*N+1, 7N+1, 11N+1 would all fit if an algorithm is well implemented!

Now here is my proposed algorithm to make 5*N+1 converges

- if your number n is even:
** n <– n /2**;** **
- if your number n is a multiply of 3:
**n<–n/3**
- else :
** n<–5*n+1**
- Repeat the algorithm until you get your number
**n **‘1’

or perhaps

- if your number n is even:
** n <– n /2**;** **
- if your number n is a multiply of 3:
**n<–n/3**
- if your number n is a multiply of 5:
**n<–n/5**
- else :
** n<–7*n+1**
- Repeat the algorithm until you get your number
**n **‘1’

Conclusion, Collatz Conjecture isn’t about 3*N+1, but it’s more about 5*N+1, 7*N+1 …. , P*N+1 where P stands for a prime number

### Like this:

Like Loading...

Read Full Post »