Is this a coincidence too?

If we write out the decimal expansion of the smaller root of f(x)=1000000x21000000x+1f(x)=1000000x^2-1000000x+1, we get the following decimal: 0.0000010000010000020000050000140.000001 \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?

Image Credit: Wikimedia Dmharvey.
×

Problem Loading...

Note Loading...

Set Loading...