Pandigital madness

The number can be manipulated to be written as ${ (1+\frac { 1 }{ { 3 }^{ { 2 }^{ 85 } } } ) }^{ { 3 }^{ { 2 }^{ 85 } } }$ which is of the form ${ (1+\frac { 1 }{ n } ) }^{ n }$ . We know that for very large $n$ , ${ (1+\frac { 1 }{ n } ) }^{ n }$ approaches $e$ .

It is an example for a pandigital number. Pandigital numbers are the numbers which have all the digits from $1$ to $9$ inclusive. $0$ is optional, sometimes it is preferred and sometimes it isn't. The above illustrated number is a very incredible formula. Incredible because it is a very good approximation for $e$ , up to $18$ trillion trillion digits. To know more about it, check this Numberphile's video.