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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}