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%I
%S 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,
%T 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,
%U 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
%N Decimal expansion of rabbit constant.
%D Schroeder, M., Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, New York: W. H. Freeman, 1991.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RabbitConstant.html">Rabbit Constant.</a>
%H Joerg Arndt: <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>, p.754 [From Joerg Arndt, Apr 15 2010]
%F Let b(n) = floor(tau*n) = A000201(n), then Rabbit Constant = Sum(a(n)/2^n, n=1..infinity)
%e .7098034...
%t 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 *)
%o (PARI) /* fast divisionless routine from fxtbook */
%o fa(y, N=17)=
%o { local(t, yl, yr, L, R, Lp, Rp);
%o /* as powerseries correct up to order fib(N+2)-1 */
%o L=0; R=1; yl=1; yr=y;
%o for(k=1, N, t=yr; yr*=yl; yl=t; Lp=R; Rp=R+yr*L; L=Lp; R=Rp; );
%o return( R )
%o }
%o a=0.5*fa(t) /* computation of 0.709803442861291314641... */
%o /* Joerg Arndt, Apr 15 2010 */
%Y Equals -1+A073115.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_
%E More terms from _Simon Plouffe_.
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