Digital Clock Times Puzzle

The Puzzle:

Digital Clock Times
Tim looked at his oven digital clock and noticed that each number was one higher than the number to its left.

He wondered: Of the 720 different clock times in a 12-hour period, how many times does this happen -- and what are the clock times?

(An example: 1:23)

Can you help Tim out?
Do you have the answer? Check against our solution!