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%I #2 Mar 30 2012 19:00:48
%S 3,5,8,11,18,26,40,58,88,130,194,287,427,633,941,1396,2074,3078,4571,
%T 6785,10073,14954,22200,32957,48926,72632,107826,160071,237631,352771,
%U 523702,777453,1154157,1713385,2543579,3776029,5605645,8321770,12353952
%N Consider the function f(n)=1/(Abs(n-r)), where r is the Dottie number, A003957. Let g(n) be defined by the recursion g(n)=Cos(g(n-1)),g(0)=1. Now, a(n)=floor(f(g(n)))
%C This sequence gives a sense of the rate of convergence to the Dottie Number.
%C Because higher values of a(n) means that g(n) is converging to the Dottie number, quick convergence means a high rate of increase for a(n).
%C This can be compared to other methods for approximation the Dottie number, by defining an analogous sequence.
%C This gives us an algorithm to measure the rate of convergence, for ANY function that convergence to a constant.
%C a(n) is asymptotically approaches an exponential regression.
%e For n=3, g(3)=cos(cos(cos(1)))
%e f(g(3))~=11.7931005 So a(3)=floor(11.7931005)=11.
%K nonn
%O 0,1
%A _Ben Branman_, Sep 12 2010
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