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A180619
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)))
0
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
OFFSET
0,1
COMMENTS
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.
EXAMPLE
For n=3, g(3)=cos(cos(cos(1)))
f(g(3))~=11.7931005 So a(3)=floor(11.7931005)=11.
CROSSREFS
Sequence in context: A308266 A320594 A227563 * A196204 A220483 A136684
KEYWORD
nonn
AUTHOR
Ben Branman, Sep 12 2010
STATUS
approved