Watch the computer walk through the digits of pi, looking for the longest runs of repeating digits. I've watched it go to 57,000 and the longest was the famous 6 9's at the 762nd place.
My son and I found https://scratch.mit.edu/projects/19826727/ promoted on pi day, 2016. We were in a computer lab and couldn't hear the digits being spoken, so we remixed it to display the digits ( https://scratch.mit.edu/projects/101658319/ ). Then we wondered when digits repeat, so I made (after a few attempts) this remix to find out. If I had more time I'd like to display a running tally of longest repetitions for all 10 digits (remix this and try! ☺).