I'm looking for the name of a data structure. It is organized like a balanced tree. The elements need not be comparable. Instead of asking if the tree contains a thing (like you would with a collection of comparables), you can query for any k'th element in logarithmic time. You can insert before or after any k'th element. So the API is a bit like a list, except all operations are logarithmic.
I think "rope" might be similar but those seem to be restricted to strings only. It could be thought of as a segment tree, where every leaf has a weight of 1, but instead of storing the weights in the leaves the entry itself is stored.
Edit: I think it could also be referred to as an "Order Statistic Tree" but without the comparison operations.