statement.md

1000-digit Fibonacci Number

Problem 25

The Fibonacci sequence is defined by the recurrence relation:

$$ F_n = F_{n-1} + F_{n-2}, \quad \text{where } F_1 = 1 \text{ and } F_2 = 1. $$

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 index of the first term in the Fibonacci sequence to contain 1000 digits?