Repunit Prime/Sequence

Sequence of Repunit Primes
The sequence of repunit primes (base $10$) begins:
 * $11, 1 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111, 11 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111, \ldots$