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March 8th, 2012, 11:51 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, 05:37 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, 08:15 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, 09:18 PM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 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 Collatzlike 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 Collatzlike sequences are quite common, and ones which work on higher digits mod some base are easy to construct. 
March 9th, 2012, 04:48 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, 10:35 PM  #6 
Newbie Joined: Apr 2012 Posts: 1 Thanks: 0  Re: Collatz conjecture & More (Please Help)
It's very easy to find such functions. 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). 
April 29th, 2012, 07:34 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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