@marnanel reminds me that when I was a kid I played the proper version of "fizzbuzz", which is more challenging than the version used as a trivial interview coding problem these days, in two ways (ok, three):

1. fizz=5 and buzz=7, not the easier 3 and 5

2. a number is eligible for 'fizz' if it is divisible by 5 _or_ has a 5 anywhere in its decimal digits, and similarly 'buzz' with 7s.

(3. because you're playing it live rather than writing code you have to use your own brain to do all the arithmetic)

#2 made the game a genuine challenge because of not losing count in the 50s, 70s, and (if you get that far) 500s, where _every_ number is 'fizz' with the occasional 'fizzbuzz', or vice versa.

But this game and your Dentist Numbers have the same blemish, which is that every play of the game is the same – in principle one could memorise the sequence. I feel as if an improvement to a game of this type would involve re-randomising some aspect of the rules every time. Hmmm.