Self-reading sequences (Q1326757)

\textit{G. Paun} and \textit{A. Salomaa} have defined [Bull. EATCS 50, 229-233 (1993)] some infinite one-sided binary strings they call ``self-reading sequences''. They left open a number of questions concerning some combinatorial properties of these sequences. We prove here a very simple lemma from which one can derive the non-ultimate periodicity of most of self-reading sequences, answering thus some of their questions. With a similar method one can prove (to appear in the same journal) that any finite word is a factor of such a sequence.