Problem 104

Pandigital Fibonacci ends

The Fibonacci sequence is defined by the recurrence relation:

F_n = F_n-1 + F_n-2, where F₁ = 1 and F₂ = 1.

It turns out that F₅₄₁, which contains 113 digits, is the first Fibonacci number for which the last nine digits are 1-9 pandigital (contain all the digits 1 to 9, but not necessarily in order). And F₂₇₄₉, which contains 575 digits, is the first Fibonacci number for which the first nine digits are 1-9 pandigital.

Given that F_k is the first Fibonacci number for which the first nine digits AND the last nine digits are 1-9 pandigital, find k.

两端为全数字的斐波那契数

斐波那契数列由如下递归关系生成：

F_n = F_n-1 + F_n-2，其中F₁ = 1且F₂ = 1。

可以发现，包含有113位数字的F₅₄₁是第一个后9位数字是1至9全数字（包含1至9所有的数字，但不一定按照从小到大的顺序）的斐波那契数，而包含有575位数字的F₂₇₄₉是第一个前9位数字是1至9全数字的斐波那契数。

若F_k是第一个前9位数字和后9位数字都是1至9全数字的斐波那契数，求k。