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In several posts of late, various laws have been taken to task. Some have been shown not to obtain on all events and others have been graced with the title undeservedly.
In my far past undergraduate days I stumbled across Bode's Law. This law was proposed long ago and is based upon numerological diddling. One starts with a series of sorts: 0, 3, 6, 12, 24, 48..... , add 4 to each term and then divide the sums by 10. The result is a series of average orbital radii in AU. Perhaps an urban fable, but it was stated that application of the law searching for a planet that wasn't there resulted in the finding of the asteroids. That served as a springboard for the theory of an exploding protoplanet.
Whatever. I am curious as to whether or not there is some basis in orbital mechanics that would produce such a startling series of radii. Any possibles?