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\begin{document}
$\begin{array}{|*{14}{@{\;}c}|}
\hline
s_1     & =     & \00   & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & \ldots        \\      % periodic 0
s_2     & =     & 1     & \01   & 1     & 1     & 1     & 1     & 1     & 1     & 1     & 1     & 1     & \ldots        \\      % periodic 1
s_3     & =     & 0     & 1     & \00   & 1     & 0     & 1     & 0     & 1     & 0     & 1     & 0     & \ldots        \\      % periodic 0,1
s_4     & =     & 1     & 0     & 1     & \00   & 1     & 0     & 1     & 0     & 1     & 0     & 1     & \ldots        \\      % periodic 1,0
s_5     & =     & 1     & 1     & 0     & 1     & \00   & 1     & 1     & 0     & 1     & 0     & 1     & \ldots        \\      % periodic 1,1,0,1,0
s_6     & =     & 0     & 0     & 1     & 1     & 0     & \01   & 1     & 0     & 1     & 1     & 0     & \ldots        \\      % 0, periodic 0,1,1
s_7     & =     & 1     & 0     & 0     & 0     & 1     & 0     & \00   & 0     & 1     & 0     & 0     & \ldots        \\      % periodic 1,0,0,0
s_8     & =     & 0     & 0     & 1     & 1     & 0     & 0     & 1     & \01   & 0     & 0     & 1     & \ldots        \\      % periodic 0,0,1,1
s_9     & =     & 1     & 1     & 0     & 0     & 1     & 1     & 0     & 0     & \01   & 1     & 0     & \ldots        \\      % periodic 1,1,0,0
s_{10}  & =     & 1     & 1     & 0     & 1     & 1     & 1     & 0     & 0     & 1     & \00   & 1     & \ldots        \\      % binary numbers 1, 10, 11, 100, 101, ...)
s_{11}  & =     & 1     & 1     & 0     & 1     & 0     & 1     & 0     & 0     & 1     & 0     & \00   & \ldots        \\      % 1 whenever new number starts in s_{10}
\vdots  &       & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots     \\
\hline
\multicolumn{10}{c}{}   \\
\hline
s       & =     & \11   & \10   & \11   & \11   & \11   & \10   & \11   & \10   & \10   & \11   & \11   & \ldots        \\
\hline
\end{array}$
\end{document}