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arXiv · 1801.07678

A simple proof of the Wirsching-Goodwin representation of integers connected to 1 in the $3x+1$ problem

Jean-Jacques Daudin·Laurent Pierre
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Abstract

This paper gives a simple proof of the Wirsching-Goodwin representation of integers connected to 1 in the $3x+1$ problem (see \cite{Wirsching} and \cite{Goodwin}). This representation permits to compute all the ascending Collatz sequences $(f^{(i)}(n),\: i=1,b-1)$ with a last value $f^{(b)}(n)=1.$ Other periodic sequences connected to $1$ are also identified.

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Jean-Jacques Daudin, Laurent Pierre. 2018-01-23. A simple proof of the Wirsching-Goodwin representation of integers connected to 1 in the $3x+1$ problem. https://arxiv.org/abs/1801.07678

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