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A003461
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Bode numbers multiplied by 10: 4 + 3*floor(2^(n-1)).
(Formerly M3302)
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6
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4, 7, 10, 16, 28, 52, 100, 196, 388, 772, 1540, 3076, 6148, 12292, 24580, 49156, 98308, 196612, 393220, 786436, 1572868, 3145732, 6291460, 12582916, 25165828, 50331652, 100663300, 201326596, 402653188, 805306372, 1610612740, 3221225476
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OFFSET
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0,1
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COMMENTS
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Bode's law is that the average distance of the n-th planet from the sun is (4 + 3*floor(2^(n-1)))/10 astronomical units.
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REFERENCES
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J. R. Newman, The World of Mathematics, Vol. I, p. 221, 1956.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Hitchhiker's Guide to the Galaxy, The Discovery of the Asteroid Belt, Dec 5, 2000, Nov 29, 2011 [Cached copy of pdf version] (The sentence that is illegible at the bottom of the second page begins "This theory is often wrongly attributed to Bode (and often cited as Bode's Law), but it was Titius that first discovered the number series for the planets, and Bode (two years later in 1778) that ...".)
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FORMULA
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a(n) = 2*a(n-1) - 4, n > 1.
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MAPLE
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A003461:=-(-4+5*z+3*z**2)/((2*z-1)*(z-1)); [Conjectured (correctly) by Simon Plouffe in his 1992 dissertation]
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MATHEMATICA
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PROG
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(PARI) a(n)=4+3*floor(2^(n-1));
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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