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projecteuler---->problem=25----1000-digit Fibonacci number

2024-07-07 17:52:27   228人阅读

问题描述：

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 first term in the Fibonacci sequence to contain 1000 digits?

翻译：

Fibonacci数列的定义如下：

Fn = Fn-1 + Fn-2，且F1 = 1, F2 = 1。

于是前12个Fibonacci数就是：

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

第十二项F12，是第一个达到三位数的Fibonacci数。

第一个达到1000位的Fibonacci数又是多少呢？


解答：

def isok(a):
    count=0
    while a>0:
        a/=10
        count+=1
    if count==1000:
        return True
    return False

a,b,c=1,1,0
count=2
while True:
    c=a+b
    count+=1
    if isok(c):
        break
    a=b
    b=c
print count




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