Using an app on another device should cancel cell phone notifications

My cell phone rings when I get a call even when I'm actively using my computer and when I answer a text on the computer, the push notification remains in the notification list on my phone. I would like for my phone to only be used for notifications if I've been idle on my computer for a while (and the idle time should be customizable) and for the push notifications to be automatically removed once I've seen them on my computer.