Question 142
The Lucas numbers are defined by $L_{0} = 2$, $L_{1} = 1$, and $L_{n+2} = L_{n+1} + L_{n}$ for every $n \geq 0$. There are $N$ integers $1 \leq n \leq 2016$ such that $L_{n}$ contains the digit $1$. Estimate $N$.
An estimate of $E$ earns $\lfloor 20 - 2|N - E| \rfloor$ or $0$ points, whichever is greater.
An estimate of $E$ earns $\lfloor 20 - 2|N - E| \rfloor$ or $0$ points, whichever is greater.