欧拉计划(python) problem 25

1000-digit Fibonacci number

Problem 25

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?

Go to the thread for problem 25 in the forum.

python code:

a,b=0,1
count=1
while b//pow(10,999)<1:
    count+=1
    a,b=b,a+b
print(count)

time: <1s