I thought of a math puzzle today and I don't yet know the answer.
Consider the binary numeral `110`. This represents the number 6.
If you interpret `110` as a base-3 numeral instead, it represents the
number 12.
12 is a multiple of 6.
Find an example like this that _does not_ end in `0`.
That is, find a sequence of zeroes and ones, whose value as a base-3
numeral, is a multiple of its value as a base-2 numeral, and which
ends in a `1`.