Problem 25 : 1000-digit Fibonacci number

Problem Statement

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?

Solution

def fibonacci():
    g=0
    i=2
    l=[1,1]
    while(g<1000):
        temp=l[i-1]+l[i-2]
        l.append(temp)
        g=len(str(temp))
        index=i
        i=i+1
        
    return index+1


print(fibonacci())

Output

4782