Question 138
Mykolka and Andriyko are playing the following game. They write positive integers turn by turn thus forming a sequence $a_1, a_2, ..., a_{2006}$ obeying the following restrictions: $a_1 = 1$ (this first turn is fixed, and it is made by Mykolka), and $a_n \le a_{n+1} \le 3a_n$ for $1 \le n \le 2005$. If, after the last turn was made, the sums $a_1 + a_2 + ... + a_{2004} + a_{2005}$ and $a_1 + a_2 + ... + a_{2005} + a_{2006}$ appear to be mutually prime numbers, then the winner is Andriyko, otherwise it is Mykolka. Who of the players can secure his victory whatever way the other one plays?