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 March 8th, 2012, 10:51 AM #1 Newbie   Joined: Mar 2012 Posts: 4 Thanks: 0 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
 March 8th, 2012, 04:37 PM #2 Senior Member   Joined: Feb 2012 Posts: 628 Thanks: 1 Re: Collatz conjecture & More (Please Help) I want a sequence that always ends in 5.
 March 8th, 2012, 07:15 PM #3 Newbie   Joined: Mar 2012 Posts: 4 Thanks: 0 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
 March 8th, 2012, 08:18 PM #4 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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.
 March 9th, 2012, 03:48 AM #5 Newbie   Joined: Mar 2012 Posts: 4 Thanks: 0 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 ?
 April 28th, 2012, 09:35 PM #6 Newbie   Joined: Apr 2012 Posts: 1 Thanks: 0 Re: Collatz conjecture & More (Please Help) It's very easy to find such functions. $f(n)= \begin{cases} \frac {3}{2} \cdot n+ 0.5 \ \ \ if \ n \ is \ odd\\ \ \ \frac {n}{2} \ \ \ \ \ \ \ \ \ \ \ if \ n \ is \ even\end{cases}$ always ends in $2,1$ (if Collatz Conjecture is true). $f(n)= \begin{cases} \frac {3}{2} \cdot n+ 1.5 \ \ \ if \ n \ is \ odd\\ \ \ \frac {n}{2} \ \ \ \ \ \ \ \ \ \ \ if \ n \ is \ even\end{cases}$ always ends in $6,3$ (if Collatz Conjecture is true). Generally ($r$ is natural number, $c$ is natural): $f(n)= \begin{cases} \frac {3}{2} \cdot 2^{r} \cdot n+ \frac {3^{c}}{2} \cdot 2^{r} \ \ \ if \ n \ is \ odd\\ \ \ \frac {n}{2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if \ n \ is \ even\end{cases}$ always ends in $2 \cdot 3^{c} \cdot 2^{r},...,3^{c}$ (if Collatz Conjecture is true).
 April 29th, 2012, 06:34 AM #7 Math Team   Joined: Apr 2012 Posts: 1,579 Thanks: 22 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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