MathDB

A sequence of integers

a_0,\ a_1,\dots a_n \dots

is defined by the following rules:

a_0=0,\ a_1=1,\ a_{n+1} > a_n

for each

n\in \mathbb{N}

, and

a_{n+1}

is the minimum number such that no three numbers among

a_0,\ a_1,\dots a_{n+1}

form an arithmetical progression. Prove that

a_{2^n}=3^n

for each

n \in \mathbb{N}.

Problem Statement