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What is Collatz Permutations and Fibonacci Numbers about?

This document discusses connections between the Collatz conjecture and the Fibonacci numbers. It shows that permutations arising from Collatz map iterations up to length 14 are enumerated by the Fibonacci numbers. Beyond length 14, excess permutations appear due to coincidences in the traces of different starting values. The document analyzes the types of steps that occur in traces and proves there are sufficient witnesses to realize all permutations up to a given length as Collatz permutations.

Author

Amalia M Olaru

Language

EN