N is a number where each digit is divisible by its place, for example:
1 has to be divisible by 1, 5 divisible by 2, 2 divisible by 3, and 7 divisible by 4.
Additionally, N must be divisible by all of its digits.
It has to be at least 5 digits long, and have at least 3 different digits.
Does N exist? Is there more than 1 number that fits N? If so is there a pattern? Give a few examples.