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A014565
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Decimal expansion of rabbit constant.
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3
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7, 0, 9, 8, 0, 3, 4, 4, 2, 8, 6, 1, 2, 9, 1, 3, 1, 4, 6, 4, 1, 7, 8, 7, 3, 9, 9, 4, 4, 4, 5, 7, 5, 5, 9, 7, 0, 1, 2, 5, 0, 2, 2, 0, 5, 7, 6, 7, 8, 6, 0, 5, 1, 6, 9, 5, 7, 0, 0, 2, 6, 4, 4, 6, 5, 1, 2, 8, 7, 1, 2, 8, 1, 4, 8, 4, 6, 5, 9, 6, 2, 4, 7, 8, 3, 1, 6, 1, 3, 2, 4, 5, 9, 9, 9, 3, 8, 8, 3, 9, 2, 6, 5
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| Schroeder, M., Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, New York: W. H. Freeman, 1991.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Joerg Arndt: Fxtbook, p.754 [From Joerg Arndt, Apr 15 2010]
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FORMULA
| Let b(n) = floor(tau*n) = A000201(n), then Rabbit Constant = Sum(a(n)/2^n, n=1..infinity)
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EXAMPLE
| .7098034...
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MATHEMATICA
| Take[ RealDigits[ Sum[N[1/2^Floor[k*GoldenRatio], 120], {k, 0, 300}]-1][[1]], 103] (* From Jean-François Alcover, Jul 28 2011, after B. Cloitre *)
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PROG
| (PARI) /* fast divisionless routine from fxtbook */
fa(y, N=17)=
{ local(t, yl, yr, L, R, Lp, Rp);
/* as powerseries correct up to order fib(N+2)-1 */
L=0; R=1; yl=1; yr=y;
for(k=1, N, t=yr; yr*=yl; yl=t; Lp=R; Rp=R+yr*L; L=Lp; R=Rp; );
return( R )
}
a=0.5*fa(t) /* computation of 0.709803442861291314641... */
/* Joerg Arndt, Apr 15 2010 */
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CROSSREFS
| Equals -1+A073115.
Sequence in context: A021589 A093444 A021858 * A073115 A176444 A197025
Adjacent sequences: A014562 A014563 A014564 * A014566 A014567 A014568
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KEYWORD
| nonn,cons
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| More terms from Simon Plouffe (simon.plouffe(AT)gmail.com).
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