MathDB

For any positive integer

x

define

g(x)

as greatest odd divisor of

x,

and f(x) \equal{} \begin{cases} \frac {x}{2} \plus{} \frac {x}{g(x)} & \text{if \ $$x$$ is even}, \\ 2^{\frac {x \plus{} 1}{2}} & \text{if \ $$x$$ is odd}. \end{cases} Construct the sequence x_1 \equal{} 1, x_{n \plus{} 1} \equal{} f(x_n). Show that the number 1992 appears in this sequence, determine the least

n

such that x_n \equal{} 1992, and determine whether

n

is unique.

Problem Statement