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

Famous quotes containing the words juggler and/or sequence:

    “We can paint unrealistic pictures of the juggler—displaying her now as a problem-free paragon of glamour and now as a modern hag. Or we can see in the juggler a real person who strives to overcome the obstacles that nature and society put in her path and who does so with vigor and determination.”
    —Faye J. Crosby (20th century)

    “We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.”
    —E.M. (Edward Morgan)