# The Collatz 3n+1 problem

Peter Donovan

## Affiliation:

University of New South Wales

## Date:

Tue, 17/04/2018 - 12:00pm to 1:00pm

## Venue:

RC-4082, The Red Centre, UNSW

## Abstract:

A positive integer $a_0$ determines recursively the sequence$a_0,a_1,a_2,\ldots$ by the Collatz rules $a_{n+1}=a_n/2$ for even $n$ and $a_{n+1}=(3a_n+1)$ for$n$ odd.  Massive electronic calculation over many years has verified that for each`start' $a_0$ examined there is an $n\ge 0$ with $a_n=1$ and so $a_{n+3}=1$, etc. Theauthor's experience in using modern computers to understand WW2 cryptology hasbeen used to find a new phenomenon in this context.