A mnemonic for the sizes of the orbits of the planets is known as the Titius-Bode Rule.

orbit size = [3N+4]/10 A.U.

where we set N = 0, 1, 2, 4, 8, 16, 32, and so on. This series of numbers has a rather straightforward definition, but is not a completely natural sequence. For Mercury, N = 0, and so a = 0.4 A.U.. Pretty close to the correct answer. For Venus, N = 1 and so a = 0.7 A. U., hmmmm. For Jupiter, N = 16, and so a = 5.2 A.U. The law works well for some planets. Further, an interesting prediction was made when the law was proposed. There was no planet for N = 8, i.e. for a = 2.8 A.U. However, subsequent work showed that there was a belt of small rocky objects near a = 2.8 A.U. (the asteroid belt). This is probably the planet predicted by the Titius-Bode relation.

Astronomers used to ignore the Titius-Bode relation as only an interesting quirk of numerics. However, although there is (as of today) no physical explanation for the law, there may be physical content in the law. It is conceivable that the Titius-Bode relation contains information on the stability properties of the orbital arrangement of the planets.