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Problem 25


Problem 25


1000-digit Fibonacci number

The Fibonacci sequence is defined by the recurrence relation:
F1 = 1 F2 = 1
Fn = Fn−1 + Fn−2

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?


一千位斐波那契数

斐波那契数列是按如下递归关系定义的数列:
F1 = 1 F2 = 1
Fn = Fn−1 + Fn−2

因此斐波那契数列的前12项分别是:
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144

第一个有三位数字的项是第12项F12

在斐波那契数列中,第一个有1000位数字的是第几项?