Search: id:A003461
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%I A003461 M3302
%S A003461 4,7,10,16,28,52,100,196,388,772,1540,3076,6148,12292,24580,49156,
%T A003461 98308,196612,393220,786436,1572868,3145732,6291460,12582916,25165828,
%U A003461 50331652,100663300,201326596,402653188,805306372,1610612740,3221225476
%N A003461 Bode numbers multiplied by 10: 4 + 3*floor(2^(n-1)).
%C A003461 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.
%C A003461 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
%D A003461 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003461 S. L. Jaki, "The Titius-Bode law: a strange bicentenary", Sky and Telescope, 
               43 (No. 5, May 1972), 280-281.
%D A003461 W. I. McLaughlin, ``Note on a tetranacci alternative to Bode's law,'' 
               preprint, 1974.
%D A003461 J. R. Newman, The World of Mathematics, Vol. I, p. 221, 1956.
%H A003461 Anonymous, <a href="http://en.wikipedia.org/wiki/Bode's_law">Bode's Law</
               a>, Wikipedia
%H A003461 BBC Corp., <a href="http://www.bbc.co.uk/dna/h2g2/%41354412">Title?</
               a>
%H A003461 M. Haynes and S. Churchman, <a href="http://astrosun.tn.cornell.edu/courses/
               astro201/bodes_law.htm">Bode's Law</a>
%H A003461 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A003461 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A003461 a(n)=2*a(n-1)-4, n>1.
%p A003461 A003461:=-(-4+5*z+3*z**2)/((2*z-1)*(z-1)); [Conjectured (correctly) by 
               S. Plouffe in his 1992 dissertation.]
%t A003461 Table[4 + 3 Floor[2^(n - 1)], {n, 0, 31}] (* Robert G. Wilson v, (rgwv(AT)rgwv.com), 
               Mar 19 2008 *)
%o A003461 (PARI) a(n)=4+3*floor(2^(n-1));
%Y A003461 Cf. A061654.
%Y A003461 First differences of A087009.
%Y A003461 Sequence in context: A153003 A128429 A131500 this_sequence A023375 A119249 
               A071415
%Y A003461 Adjacent sequences: A003458 A003459 A003460 this_sequence A003462 A003463 
               A003464
%K A003461 nonn,easy,nice
%O A003461 0,1
%A A003461 N. J. A. Sloane (njas(AT)research.att.com), W. I. McLaughlin
%E A003461 Description corrected by Michael Somos

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