OP here -- I think I've satisfied myself that the answer to my question is: "There isn't one, really".
There is the set of "Internet Safe Colors", which start from 00 00 00 and add 33 hex to each of the red, green, and blue values in turn to get a set of RGB colors; this is the KIND of algorithm I was looking for, but the resulting colors are not always easily distinguishable from each other, and the 33 hex appears arbitrary, chosen for its calculation convenience as opposed to anything about the resulting colors.
There's the "X11 color" set, which (according to Wikipedia) is just a set that's been included in X installations for so long no one really remembers where it came from. The latter's primary purpose appears to be to map each color to a name so it can be specified by name. I have not detected a
pattern to the numbers that result in the colors that I can use to calculate them.
Someone pointed out that regular JPG files only have 256 colors, and that asking to get 100 that were all distinct is likely a tall order. It's good to keep that in mind.
So I'm back to storing a list of colors for what I want to do, and going through the tedious job of choosing such colors (something I wish I had more talent for).
I discovered an additional requirement -- since I am putting text in the same box as the color, I need the color to be light enough that black text will show up reasonably well.
Thanks to all that posted -- I did learn things about colors from the suggestions and code posted here. If someone's really interested, I'll post my set of colors when I feel like I've got a reasonable set.
rc