Mixing time of the card-cyclic-to-random shuffle

The card-cyclic-to-random shuffle on n cards is defined as follows: at time t remove the card with label t mod n and randomly reinsert it back into the deck. Pinsky [Probabilistic and combinatorial aspects of the card-cyclic-to-random shuffle (2011). Unpublished manuscript] introduced this shuffle and asked how many steps are needed to mix the deck. He showed n steps do not suffice. Here we show that the mixing time is on the order of .(nlogn)