Question 24
Let $T_1=1$, $T_2=1+\dfrac11$, $T_3=1+\dfrac1{1+\frac11}$, $\ldots$, and $T_n=1+\dfrac1{T_{n-1}}$ for $n\ge2$. Write $T_n=\dfrac{P_n}{Q_n}$ in simplest form, where $P_n,Q_n$ are coprime positive integers. How many of $P_1,P_2,\ldots,P_{2019}$ are odd?
Answer format: an integer without units. Leading zeros are optional; the source uses four digit boxes.
Answer format: an integer without units. Leading zeros are optional; the source uses four digit boxes.