## [Math] Collatz conjecture

26 02 2016

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 ‘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 ‘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

9 01 2012