Is there anyway to detect home button has been pressed (switching on the phone) or lock screen is active?

I have an idea to make a game (simple puzzle game) run after switching on the phone (or pressing the home button). This game also can run automatically when phone (android) startup. I have looked from some questions but I cant find that has same problem with me, that is a game that will runs after switching on the phone AND runs automatically when phone startup. Is there any idea to do it?

Thank you

Sorry if my english is bad