diff --git a/project_euler/problem_25/sol3.py b/project_euler/problem_25/sol3.py new file mode 100644 index 000000000..4e3084ce5 --- /dev/null +++ b/project_euler/problem_25/sol3.py @@ -0,0 +1,57 @@ +# -*- coding: utf-8 -*- +""" +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? +""" + + +def solution(n): + """Returns the index of the first term in the Fibonacci sequence to contain + n digits. + + >>> solution(1000) + 4782 + >>> solution(100) + 476 + >>> solution(50) + 237 + >>> solution(3) + 12 + """ + f1, f2 = 1, 1 + index = 2 + while True: + i = 0 + f = f1 + f2 + f1, f2 = f2, f + index += 1 + for j in str(f): + i += 1 + if i == n: + break + return index + + +if __name__ == "__main__": + print(solution(int(str(input()).strip())))