Finding reproducible articles
I would suggest graduate level textbooks for that. They often leave proofs or part of it to the reader and some of them even have exercises, allowing you to learn the new topic by actually working on it. Furthermore, they made sure that what they left open is solvable in an appropriate amount of time.
Another nice point is that they often discuss the most important theories and concepts in a field, where on the other hand a paper might be focused on a very tiny topic.

There are textbooks for many different levels (starting at undergraduate and going as far as to being interesting to a professor who wants to extend his knowledge to a new field), depending on how much you already know.