====== Juggler sequences ======

//Juggler sequences //were first proposed by American mathematician and author [[http://www.pickover.com/|Clifford A. Pickover. ]] They take the form :

$${\displaystyle a_{k+1}={\begin{cases}\left\lfloor a_{k}^{\frac {1}{2}}\right\rfloor {\mbox{if }}a_{k}{\mbox{ is even}}\\\\\left\lfloor a_{k}^{\frac {3}{2}}\right\rfloor {\mbox{if }}a_{k}{\mbox{ is odd}}.\end{cases}}}$$

It's conjectured that all Juggler Sequences eventually reach 1. The sequences have been verified for initial terms up to 10<sup>6</sup> - but the conjecture has yet to be proved or disproved.

Technical details [[https://mathworld.wolfram.com/JugglerSequence.html|Wolfram Mathworld]]

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Also see : [[content:mathematics:collatz_conjecture]]