MathDB

Initially, Alice is given a positive integer

a_0

. At time

i

, Alice has two choices,

\begin{cases}a_i\mapsto\frac1{a_{i-1}}\\a_i\mapsto2a_{i-1}+1\end{cases}

Note that it is dangerous to perform the first operation, so Alice cannot choose this operation in two consecutive turns. However, if

x>8763

, then Alice could only perform the first operation. Determine all

a_0

so that

\{i\in\mathbb N\mid a_i\in\mathbb N\}

is an infinite set.

Problem Statement