Analyzing the Stopping Time of Collatz Sequences

by Brock Lewis

Submitted : Fall 2012

In this study I wrote a computer program in MATLAB for calculating the iterations required for a Collatz sequence to halt, and then I analyzed a small set of relatively large numbers. The numbers I put through my program were one trillion and one through one trillion and fifty. I found that all of the numbers had very similar stopping times—in fact, there were only four different stopping times for all fifty numbers; 146, 239, 203, and 296. Discovering this leads me to advise future researchers to utilize similar computer programs—and certainly computers in general—for their research endeavors. Techniques like this can and should be utilized, not only for Collatz sequences, but for any sequence, and in general, for all complex mathematical problems.

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