I once (years ago) considered writing a mobile app as a learning project for school to give me notifications of new posts, but realized that the api really should support a couple of functions first.

- Number of new entries on reading page since time x
- Number of new entries on subscription filter y since time x
- List of subscription filters for my account

Those would allow displaying the number of new posts on mobile's front screen easily and setting up which number should be displayed on the mobile app.

Using push notifications for that would be extra nice, but I know nothing about them, being a noob. :)