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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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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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.
The Titius-Bode Law is a rough rule that predicts the spacing of the planets in the Solar System. The relationship was first pointed out by Johann Titius in 1766 and was formulated as a mathematical expression by J. E. Bode in 1778. It lead Bode to predict the existence of another planet between Mars and Jupiter in what is now called the asteroid belt. - Robert G. Wilson v, (rgwv(AT)rgwv.com), Mar 19 2008
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REFERENCES
| S. L. Jaki, "The Titius-Bode law: a strange bicentenary", Sky and Telescope, 43 (No. 5, May 1972), 280-281.
W. I. McLaughlin, ``Note on a tetranacci alternative to Bode's law,'' preprint, 1974.
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
| Anonymous, Bode's Law, Wikipedia
BBC Corp., Title?
M. Haynes and S. Churchman, Bode's Law
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index to sequences with linear recurrences with constant coefficients, signature (3,-2)
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FORMULA
| a(n)=2*a(n-1)-4, n>1.
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MAPLE
| A003461:=-(-4+5*z+3*z**2)/((2*z-1)*(z-1)); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[4 + 3 Floor[2^(n - 1)], {n, 0, 31}] (* Robert G. Wilson v, (rgwv(AT)rgwv.com), Mar 19 2008 *)
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PROG
| (PARI) a(n)=4+3*floor(2^(n-1));
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CROSSREFS
| Cf. A061654.
First differences of A087009.
Sequence in context: A128429 A191154 A131500 * A023375 A119249 A071415
Adjacent sequences: A003458 A003459 A003460 * A003462 A003463 A003464
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), W. I. McLaughlin
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EXTENSIONS
| Description corrected by Michael Somos
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