PDF reader on iOS with autosync

Usually I find ebooks/PDF I want to read while browsing on my PC from work or my Mac at home. I'd like to send them to Dropbox (or any other service) and have them automatically sync to my iPad so I can read them offline while commuting to home/work. My iPad is always connected to WiFi while I am at work or home.

iOS apps can't run in the background constantly to do this task.

Dropbox can do this if you're willing to open the app whilst on network. Add the PDFs to a folder on your Dropbox, then in the app, choose Make Available Offline for that folder.

In the future, you can add files to that folder on your computer, then simply open the app on your iOS device to load the PDFs.