I haven’t done the others yet, but I might get round to it. An interesting one is the number of n period siteswaps in a given number of places for pi. "What would that look like?" I hear you ask. Well, in the first 100,000 digits of pi, here are the frequencies of the different siteswap periods:
n frequency
1 100000
2 48910
3 22496
4 9328
5 3842
6 1673
7 642
8 260
9 95
10 37
11 6
12 4
13 5
A graph of which can be found here: <ntlworld.com> You’ll notice that the log graph is very linear (except at one end, but that’s because the frequencies get smaller - this would be fixed by examining more digits).—Guy