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:

    “If the juggler is tired now, if the broom stands
    In the dust again, if the table starts to drop
    Through the daily dark again, and though the plate
    Lies flat on the table top,
    For him we batter our hands
    Who has won for once over the world’s weight.”
    —Richard Wilbur (b. 1921)

    “Reminiscences, even extensive ones, do not always amount to an autobiography.... For autobiography has to do with time, with sequence and what makes up the continuous flow of life. Here, I am talking of a space, of moments and discontinuities. For even if months and years appear here, it is in the form they have in the moment of recollection. This strange form—it may be called fleeting or eternal—is in neither case the stuff that life is made of.”
    —Walter Benjamin (1892–1940)