The Fibonacci sequence is defined by the recurrence relation:

Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1. Hence the first 12 terms will be:

F1 = 1 F2 = 1 F3 = 2 F4 = 3 F5 = 5 F6 = 8 F7 = 13 F8 = 21 F9 = 34 F10 = 55 F11 = 89 F12 = 144 The 12th term, F12, is the first term to contain three digits.

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

from time import time
def fib(n):
 """returns index of the first fibonacci of length n digits."""
 fibs = [0, 1]
 while len(str(fibs[-1])) < n:
 fibs.append(fibs[-1] + fibs[-2])
 return len(fibs) - 1
if __name__ == '__main__':
 time1 = time()
 print(fib(1000))
 print(f'Time: {time() - time1} seconds.')

The Fibonacci sequence is defined by the recurrence relation:

F_n = F_n−1 + F_n−2, where F₁ = 1 and F₂ = 1.

Hence the first 12 terms will be:

F₁ = 1
F₂ = 1
F₃ = 2
F₄ = 3
F₅ = 5
F₆ = 8
F₇ = 13
F₈ = 21
F₉ = 34
F₁₀ = 55
F₁₁ = 89
F₁₂ = 144

The 12th term, F₁₂, is the first term to contain three digits.

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

from time import time
def fib(n):
 """returns index of the first fibonacci of length n digits."""
 fibs = [0, 1]
 while len(str(fibs[-1])) < n:
 fibs.append(fibs[-1] + fibs[-2])
 return len(fibs) - 1
if __name__ == '__main__':
 time1 = time()
 print(fib(1000))
 print(f'Time: {time() - time1} seconds.')