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Problem 104


Problem 104


Pandigital Fibonacci ends

The Fibonacci sequence is defined by the recurrence relation:

Fn = Fn-1 + Fn-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 Fk 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:

Fn = Fn-1 + Fn-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Fk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。