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March 8th, 2012, 10:51 AM   #1
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Collatz conjecture & More (Please Help)

http://en.wikipedia.org/wiki/Collatz_conjecture
First i would like everyone to know about 3n+1 conjecture or more popularly known as Collatz Conjecture

Here What ever you put in the function it ultimately comes to 1 after a finite number of times

My Question is Simple ?
Have any one found out the function which is similar to collatz conjecture but always ends in 2
Have any one found out the function which is similar to collatz conjecture but always ends in 3
Have any one found out the function which is similar to collatz conjecture but always ends in 4

If not i think i found them
Please tell me that am i the first one to discover them

Post here if you have any questions
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March 8th, 2012, 04:37 PM   #2
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Re: Collatz conjecture & More (Please Help)

I want a sequence that always ends in 5.
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March 8th, 2012, 07:15 PM   #3
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Re: Collatz conjecture & More (Please Help)

No I have not found out a function which ends in 5
I have only for 2 , 3 , 4, 6 Only

No ALL I WANT TO KNOW THAT AM I THE FIRST PERSON IN THE WORLD TO DISCOVER THIS or some one else already did it

Please guys help me out with this
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March 8th, 2012, 08:18 PM   #4
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Re: Collatz conjecture & More (Please Help)

There are lots of functions which are Collatz-like but leave the last digit untouched (or set it to some predefined value). The easiest example would just work on floor(n/10), multiply the result by 10, and add 2 (or whatever).

But more generally, the Collatz conjecture arises naturally in the study of Turing machines, even ones as small as 5 states. So it's easy to imagine that Collatz-like sequences are quite common, and ones which work on higher digits mod some base are easy to construct.
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March 9th, 2012, 03:48 AM   #5
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Re: Collatz conjecture & More (Please Help)

So what is the end story
some one already did it , right

So What is the Function Which always Leads to 2 or 3 or 4
Please Provide me the functions so that i can match them with mine

:::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::;
Not Related to the Above:

I am talking about properties just like collatz
eg:Collatz 3n+1 Conjecture
f(n)=
n=odd -> 3n+1
n=even -> n/2

f{f{f{...k times..}}}=1
k is finite
n>0
Even
if you start with 1
it goes like 1 ->4->2->1

My eg,

f(n)=
n=odd -> some function
n=even -> some function

f{f{f{...j times...}}} = 3
j is finite
n>2 any number you like
It also takes values 1 and 2 which ends up as 2 too

So is the function you described is like this (2nd Example) ?
and it is easy to make ? how to make this please elaborate ?
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April 28th, 2012, 09:35 PM   #6
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Re: Collatz conjecture & More (Please Help)

It's very easy to find such functions.


always ends in (if Collatz Conjecture is true).


always ends in (if Collatz Conjecture is true).

Generally ( is natural number, is natural):


always ends in (if Collatz Conjecture is true).
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April 29th, 2012, 06:34 AM   #7
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Re: Collatz conjecture & More (Please Help)

The Collatz procedure itself will always hit 4 and 2 before hitting 1 - unless you start the procedure at 0.
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