# Sequenta

The sequence $a_n$ of real numbers is defined as follows: $a_0 = \frac {6} {7}$ and $$a_ {n + 1} = \begin {cases} 2a_n & \mbox {if} a_n <\frac {1 } {2} \\ 2a_n-1 & \mbox {if} a_n \geq \frac {1} {2} \end {cases}$$ The value $a_ {2020}$ can be represented as the irreducible fraction $\frac {m} {n}$, where $m$ and $n$ are natural numbers. What is $m + n$ equal to?