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))).

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

Author

Ben Branman, Sep 12 2010

Keywords

• nonn

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.

Examples

			For n=3, g(3)=cos(cos(cos(1)))
f(g(3))~=11.7931005 So a(3)=floor(11.7931005)=11.