During a garage sale I saw a strange old electronic device (not really, it's just flavor story). It had a battery slot, a button and a row of seven-segment displays - though from all except the two last digits the magic smoke had clearly escaped. Curious, I bought it for a dollar, took it home and put in a battery. Right away a single-digit number showed on the display (not a 7). I pressed the button, and the number changed. Trying it a few more times, I noticed a pattern to the numbers: it always went
97, 65, 85, 67, 15, 35, 37, 65, 85, 07, 15, 35, 77, 65, 85, 47, 15, 35, 17, 65, 85, 87, 15, 35, 57, 65, 85, 27, 15, 35.
After a while I got bored, so I threw the device away. However, it has been nagging at me what rule might be underlying the pattern of this number sequence. Maybe you know?