Question 14
(POL 2) For any positive integer $x$ define $g(x)$ to be the greatest odd divisor of $x$; $f(x)=x/2+x/g(x)$ if $x$ is even, and $f(x)=2^{(x+1)/2}$ if $x$ is odd.
Construct the sequence $x_1=1$, $x_{n+1}=f(x_n)$. Show that the number $1992$ appears in this sequence, determine the least $n$ such that $x_n=1992$, and determine whether $n$ is unique.
Construct the sequence $x_1=1$, $x_{n+1}=f(x_n)$. Show that the number $1992$ appears in this sequence, determine the least $n$ such that $x_n=1992$, and determine whether $n$ is unique.