Juggler sequence
In number theory, 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 = { ⌊ a k 1 2 ⌋ , if a k is even ⌊ a k 3 2 ⌋ , if a k is odd . {\displaystyle a_{k+1}={\begin{cases}\left\lfloor a_{k}^{\frac {1}{2}}\right\rfloor ,&{\text{if }}a_{k}{\text{ is even}}\\\\\left\lfloor a_{k}^{\frac {3}{2}}\right\rfloor ,&{\text{if }}a_{k}{\text{ is odd}}.\end{cases}}} == Background == Juggler sequences were publicized by American mathematician and author Clifford A. Pickover.