A positive integer $n$ is called pandigital , if every digit from $0$ to $9$ occurs in the decimal expansion of $n$.
Conjecture : The largest non-pandigital fibonacci-number (a fibonacci-number with at least one digit missing in the decimal expansion) is $F_{285}$. This is true upto $F_{10^4}$.
Can this conjecture be proven ?
But I am mainly interested in another construction : We collect the prime factors of the fibonacci-number $F_n$ and look whether the concattenation of those leads to a pandigit-number (in other words , every digit from $0$ to $9$ occurs in at least one of the prime factors). Let us call such a fibonacci-number good , otherwise bad.
What is the largest bad fibonacci-number ? I guess that the number of bad fibonacci-numbers is finite since the concattenation of the prime factors will in almost all cases be not significantly smaller than the number of digits of $F_n$ itself.
No prime factor of $F_{312}$ has digit $6$. Upto $F_{380}$ this is the largest such fibonacci-number. Hence the largest "bad" fibonacci-number might be $F_{312}$.