### User Tools

To create and edit articles, please register and log-in

Click categories to expand

A-Z listingplugin-autotooltip__plain plugin-autotooltip_bigA-Z listing

This is an alphabetical index of all content pages.

Other categories

Utilities

Also see

Wikenigma supports:

Auto-Translate Site
Indexed under : Mathematics

# Collatz conjecture

Using the formula :

$${\displaystyle f(n)={\begin{cases}{\frac {n}{2}}\quad\quad\quad{\text{if }}n\equiv 0{\pmod {2}}\\[4px]3n+1\quad{\text{if }}n\equiv 1{\pmod {2}}.\end{cases}}}$$

The Collatz conjecture states that this process will eventually reach the number 1, regardless of which positive integer is chosen initially.

For example, using n = 12 generates the sequence 12, 6, 3, 10, 5, 16, 8, 4, 2, 1.

The conjecture remains open : i.e. neither proven or disproven.

Also see : Juggler sequencesplugin-autotooltip__plain plugin-autotooltip_bigJuggler sequences

Juggler sequences were first proposed by American mathematician and author Clifford A. Pickover. They take the form :

{\displaystyle a_{k+1}={\begin{cases}\left\lfloor a_{k}^{\frac {1}{2}}\right\rfloor {\mbox{if }}a_{k}{\mbox{ is even}}\\\\\left\l…

## Dear reader : Do you have any suggestions for the site's content?

Ideas for new topics, and suggested additions / corrections for old ones, are always welcome.

If you have skills or interests in a particular field, and have suggestions for Wikenigma, get in touch !

Or, if you'd like to become a regular contributor . . . request a login password. Registered users can edit the entire content of the site, and also create new pages.

( The 'Notes for contributors' section in the main menu has further information and guidelines etc.)

## Automatic Translation

You are currently viewing an auto-translated version of Wikenigma

Please be aware that no automatic translation engines are 100% accurate, and so the auto-translated content will very probably feature errors and omissions.

Nevertheless, Wikenigma hopes that the translated content will help to attract a wider global audience.

Show another (random) article

### Page Tools

DOKUWIKI IMPLEMENTATION DESIGN BY UNIV.ORG.UK MAY 2022