Overview

Question

The Fibonacci sequence is defined by the recurrence relation:

$F_n = F_{n−1} + F_{n−2} \text{ where } F_1 = 1 \text{ and } F_2 = 1$

Hence the first 12 terms will be:

\begin{aligned} F_1 &= 1 \\\\ F_2 &= 1 \\\\ F_3 &= 2 \\\\ F_4 &= 3 \\\\ F_5 &= 5 \\\\ F_6 &= 8 \\\\ F_7 &= 13 \\\\ F_8 &= 21 \\\\ F_9 &= 34 \\\\ F_{10} &= 55 \\\\ F_{11} &= 89 \\\\ F_{12} &= 144 \end{aligned}

The 12th term, $$F_{12}$$, is the first term to contain three digits.

What is the first term in the Fibonacci sequence to contain 1000 digits?

4782