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Published November 26, 2014 | Version v1
Working paper Open

Why do Collatz series converge?

Creators

  • 1. University of Leicester

Description

The aim of this study was to investigate why Collatz series, starting with positive whole numbers, always seem to converge (i.e. end in the 4,2,1 cycle), regardless of their initial behaviour. The results presented here appear to show that symmetrical, Gaussian-like distributions may be inherently involved in the generation of these sequences. The Collatz process appears to draw at random (although not proven or tested in this preliminary report) from this distribution, presumably resulting in its convergent behaviour. It is noted that this is not an attempt or claim to prove or disprove the Collatz conjecture, but only a collection of the results obtained in the aforementioned investigation.

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Why_do_Collatz_series_converge.pdf

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