Definition:Juggler Sequence

Theorem
Let $m \in \Z_{\ge 0}$ be a positive integer.

The juggler sequence on $m$ is defined recursively as:
 * $J_m \left({n}\right) = \begin{cases} m & : n = 0 \\

\left\lfloor{\sqrt {J_m \left({n - 1}\right)} }\right\rfloor & : n \text{ even} \\ \left\lfloor{\sqrt {\left({J_m \left({n - 1}\right)}\right)^3} }\right\rfloor & : n \text{ odd} \end{cases}$ where:
 * $\left\lfloor{x}\right\rfloor$ denotes the floor of $x$
 * $\sqrt x$ denotes the positive square root of $x$.