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`

.