If we write out the decimal expansion of the smaller root of \(f(x)=1000000x^2-1000000x+1\), we get the following decimal: \[0.000001 \quad 000001\quad 000002\quad 000005 \quad 000014 \quad \ldots\] which we notice as the first 5 Catalan numbers. How many distinct Catalan numbers occur in a row before this pattern stops?
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