Proving that terms of sequence are not divisible by 4
Source: Balkan MO ShortList 2008 N3
April 5, 2020
Problem Statement
The sequence is defined as follows
\begin{align*} \chi_{n+1}=\chi_n + \chi _{\lceil \frac{n}{2} \rceil} ~, \chi_1 =1 \end{align*}
Prove that none of the terms of this sequence are divisible by