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A180619
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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)))
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0
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3, 5, 8, 11, 18, 26, 40, 58, 88, 130, 194, 287, 427, 633, 941, 1396, 2074, 3078, 4571, 6785, 10073, 14954, 22200, 32957, 48926, 72632, 107826, 160071, 237631, 352771, 523702, 777453, 1154157, 1713385, 2543579, 3776029, 5605645, 8321770, 12353952
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OFFSET
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0,1
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COMMENTS
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This sequence gives a sense of the rate of convergence to the Dottie Number.
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).
This can be compared to other methods for approximation the Dottie number, by defining an analogous sequence.
This gives us an algorithm to measure the rate of convergence, for ANY function that convergence to a constant.
a(n) is asymptotically approaches an exponential regression.
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LINKS
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EXAMPLE
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For n=3, g(3)=cos(cos(cos(1)))
f(g(3))~=11.7931005 So a(3)=floor(11.7931005)=11.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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