Pandigital approximations to $e$
You can extend your idea to higher bases to get as accurate as you like. For example in base $N=2^{3456789}+1$:
$$\Large{\left({1+(2^{3456789}})^{(10-11)^{(-12+13)\cdots(-(N-2)+(N-1))}}\right)}^{N}$$
You can extend your idea to higher bases to get as accurate as you like. For example in base $N=2^{3456789}+1$:
$$\Large{\left({1+(2^{3456789}})^{(10-11)^{(-12+13)\cdots(-(N-2)+(N-1))}}\right)}^{N}$$