Aperiodic recurrent sequence
Source: Czech and Slovak Olympiad 1990, National Round, Problem 1
October 12, 2024
algebraSequencesrecurrence relationperiodic
Problem Statement
Let be a sequence given by
\begin{align*}
a_1 &= 1, \\
a_{2^k+j} &= -a_j\text{ for any } k\ge0,1\le j\le 2^k.
\end{align*}
Show that the sequence is not periodic.