Sequence of Smallest Numbers whose Reciprocal has Period n

Theorem
Let $\left\langle{s_n}\right\rangle$ be the sequence defined as:
 * $s_n$ is the smallest positive integer the decimal expansion of whose reciprocal has a period of $n$

for $n = 0, 1, 2, \ldots$

Then $\left\langle{s_n}\right\rangle$ begins:
 * $1, 3, 11, 27, 101, 41, 7, 239, 73, 81, 451, \ldots$

Proof
Demonstrated by inspection and calculation: