This is just speculation, but I think a plausible model that could explain these numbers is the following:
* First, after each herb update, you roll a die. We know that TB likes dice. I don't know the kind of die, but let's suppose that it's 1d20, for example. We call the obtained number T, the "checking period" for herb generation.
* Every T turns, there is a check with a given probability P of herbs being updated. On the turn where herbs are updated, we re-roll P for the next generation.
This could account for these patterns in the data, because turns with many divisors in the 1-20 range would be more likely to appear, as they would be checked for more possible values of T (the first roll) than turns with few divisors in that range.