Number Theory


Partitioning the Positive Integers with the Collatz Algorithm

Authors: James Edwin Rock

Collatz sequences are formed by applying the Collatz algorithm to a positive integer. If it is even repeatedly divide by two until it is odd, then multiply by three and add one to get an even number and vice versa. Eventually you get back to one. The Collatz Structure is created, which contains all positive integers exactly once. The terms of the Collatz Structure are joined together via the Collatz algorithm. Thus, every positive integer forms a Collatz sequence with unique terms terminating in the number one.

Comments: 5 Pages. Copyright 2018 James Edwin Rock Create Commons Attribution-ShareAlike 4.0 International License

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[v1] 2018-12-07 13:32:39

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