Bode's law, Titius-Bode law

A mathematical formula that generates, along with a reasonable amount of accuracy, semimajor axes of the planets in order out from the Sun. Write the sequence

 0, 3, 6, 12, 24, ...  

and add up 4 into each of term:

 4, 7, 10, 16, 28, ...

Then divide each of the term through 10. This leaves you with the series  

0.4, 0.7, 1.0, 1.6, 2.8, ...

 that is intended to give you the semimajor axes of the planets measured in astronomical units.

Bode's law contain no theoretical justification while it was first introduced; it did, though, agree with the soon-to-be-discovered planet Uranus' orbit (19.2 au actual; 19.7 au predicted). Likewise, it predicted a missing planet among Mars & Jupiter, and shortly after that the asteroids were found in very alike orbits (2.77 au actual for Ceres; 2.8 au predicted). However, the series seems to skip onto Neptune's orbit. The form of Bode's law (i.e. a roughly geometric series) is not astonishing, in view of our theories on the formation of solar systems, but its specific formulation are thought of as coincidental.