Say I'm driving, see a 'bright sky' but no plume etc, no noise, just the sky brightening, how close would the probable detonation be? Count the seconds flash to bang. Close enough to five seconds per mile or three seconds per kilometer.
Just like lightning, only hopefully a longer count...
Don't look at the blast, if possible, you could suffer flash burns of the retina. If possible, put a major terrain feature (like a hill) between you and detonation if you are within 3-5 miles....depending on size. There is a formula for measuring the blast size by measuring the angle from ground to top of mushroom cloud, I just don't have it right now. Effective downwind drift is the killer as far as lethal radiation goes. That's why it's important to figure wind direction and speed relative to your position.
IIRC sound travels at about 330 meters per second. That's pretty close to your formula.