MathDB

Octavio writes an integer

n \geq 1

on a blackboard and then he starts a process in which, at each step he erases the integer

k

written on the blackboard and replaces it with one of the following numbers: 3k-1, 2k+1, \frac{k}{2}. provided that the result is an integer.
Show that for any integer

n \geq 1

, Octavio can write on the blackboard the number

3^{2023}

after a finite number of steps.

Problem Statement