If I just bought a game on Playstation Network can I download it on an other PS4 and play with another account?
I tried it with PS3 and it didn't work, so I asked myself maybe they fixed something new.
Yes, you can. To do this, the account that bought the game must set the second PS4 as its "primary" PS4. (Settings --> PSN --> "Activate as Your Primary PS4"
) Anyone on the second PS4 will be able to play games that your main account has downloaded to it. Your main account can still download and play its games on any PS4 by simply signing in and downloading them, so setting the second PS4 as your "primary" one won't change anything for you on the first PS4.
Sources:
http://us.playstation.com/ps4/features/ps4-faq/
http://www.playstationlifestyle.net/2013/10/28/sony-explains-how-digital-game-sharing-works-on-the-ps4-primary-system-benefits-detailed/