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.