project Eulert 学习笔记 之 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?

 解题思路：题目给出了一个斐波那契数列，要求求出第一个位数达到1000位的数的索引：

程序是这样的：

f = {}
f[0] = 1
f[1] = 1
for n in range(2,100000,1):
    f[n] = f[n - 1] + f[n - 2]
    s = str(f[n])
    numlist = [int(s[item: item + 1]) for item in range(0, len(s), 1)]
    if len(numlist) < 1000:
        print(n+2)

"""
思路:
定义f[0],f[1]
第3个数等于第1个加第2个的和
将结果转换为字符
将字符转换为N个组
统计共有多少位
小于1000位的F[n]加上2（f[0]和f[1]）就是要求的f[n]
"""