How to make a GtkButton respond to a key press

[Michael Torrie <torriem gmail com>]

Maybe I'm just not reading right, but I cannot figure out how to make a
GtkButton respond to a single key press.  For example, if I made a
simple calculator like the one that comes with Gnome, how can I make it
so when I press '1' on my keyboard, the 1 button presses.  I know how to
make shortcuts with a control key by just putting in an & in the label.
 But not just a bare key press.  Also is it possible to programmatically
depress and then release a GtkButton, simulating a click?  I'd like to
do this to generate some user feedback when the keyboard is used, while
allowing one to still click with a mouse (or finger or whatever) on the
GtkButton.

Pointing me at the right docs would be appreciated.  Gtk3 is fine.