## Pandigital Fibonacci ends

### Problem 104

Published on Friday, 9th September 2005, 06:00 pm; Solved by 10032; Difficulty rating: 25%The Fibonacci sequence is defined by the recurrence relation:

F_{n}= F_{n−1}+ F_{n−2}, where F_{1}= 1 and F_{2}= 1.

It turns out that F_{541}, 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 F_{2749}, 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*.