Juggler Sequence

In recreational mathematics a juggler sequence is an integer sequence that starts with a positive integer a0, with each subsequent term in the sequence defined by the recurrence relation:

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}

Read more about Juggler Sequence:  Background

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    —Faye J. Crosby (20th century)

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    —Walter Benjamin (1892–1940)