"She was accustomed to write to me once a week."
Translation:Ŝi kutimis skribi al mi unu fojon semajne.
English has merged the former dative and accusative cases into a single objective case that can be used for the direct or the indirect object.
The indirect object often has a "to" in front of it but not always, as in the "write me".
It's still an indirect object, though (you are still the recipient, not the thing that comes out of her pen).
Esperanto doesn't have this merger; min is only accusative / direct object, not also dative / indirect object.