Project Euler Problem 025

# Statement

The Fibonacci sequence is defined by the recurrence relation:

(1)\begin{align} F_{n} = F_{n−1} + F_{n−2},\ where\ F_{1} = 1\ and\ F_{2} = 1. \end{align}

Hence the first 12 terms will be:

Unsupported math environment "flushleft"

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?

# Solution

In a language like Python where you can handle numbers of 1000 digits easily then:

if __name__ == '__main__': i1 = 1 i2 = 1 index = 2 while len(str(i2)) < 1000: index += 1 i1, i2 = (i2, i1 + i2) print("The result is:", index)

The Python file is available for download here.