Archive for June 5th, 2008

Collatz conjecture

Thursday, June 5th, 2008

Who says all the unsolved math problems are difficult to phrase?
The Collatz conjecture can be phrased as a simple question: Start with a positive number. If the number is even take its half otherwise take 3 times the number plus 1. Now do this over and over again. The (yet unanswered) question is: will this process allways reach the number 1?
(from there the sequence of numbers gets into a boring 1, 4, 2, 1,… cycle)
The conjecture is “yes” and it has been shown to be true for numbers up to 10 * 258, but this is of course no big evidence.
The above image shows the numbers when starting with 353. It takes 125 iterations to reach 1 in this case and the biggest intermediate value is 9232.
There are some nice reformulations of the problem. One can for example state it as a a 2-tag system
The 2-tag sequence for 7 follows below