Since you can’t have siteswaps with two digits n places apart where the first digit is the second digit plus n[1], it should be easy to find a lot of such pairs in whatever section of pi you’re looking at, so limiting the maximum length of a siteswap to the largest distance between these pairs. Actually it would be from the digit after the first digit in the first pair to the digit before the second digit in the second pair.

For example in 3.1415926535897932384 (twenty digits) there can be no                       ^^ ^^ siteswap of period > 8 because it would have to include 65 or 32, which aren’t allowed.—Rory