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. Evaluating the Titius-Bode Rule we find,

Planet	Titius-Bode Rule (A.U.)	Actual (A.U.)
Mercury	0.4	0.387
Venus	0.7	0.723
Earth	1	1
Mars	1.6	1.524
asteroids	2.8	2.8
Jupiter	5.2	5.203
Saturn	10	9.554
Uranus	19.6	19.22
Neptune	38.8	30.11
Pluto	77.2	39.54

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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). Is this the planet predicted by the Titius-Bode relation?

Astronomers tend to ignore the Titius-Bode Rule, as only an interesting quirk of numerics. There is no physical explanation for the Rule, but there may be physical content in the law. It is conceivable that the Titius-Bode Rule contains information on the stability properties of the orbital arrangement of the planets.