This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A180619 #4 Jun 02 2025 03:04:21 %S A180619 3,5,8,11,18,26,40,58,88,130,194,287,427,633,941,1396,2074,3078,4571, %T A180619 6785,10073,14954,22200,32957,48926,72632,107826,160071,237631,352771, %U A180619 523702,777453,1154157,1713385,2543579,3776029,5605645,8321770,12353952 %N 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))). %C A180619 This sequence gives a sense of the rate of convergence to the Dottie Number. %C A180619 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 A180619 This can be compared to other methods for approximation the Dottie number, by defining an analogous sequence. %C A180619 This gives us an algorithm to measure the rate of convergence, for ANY function that convergence to a constant. %C A180619 a(n) is asymptotically approaches an exponential regression. %e A180619 For n=3, g(3)=cos(cos(cos(1))) %e A180619 f(g(3))~=11.7931005 So a(3)=floor(11.7931005)=11. %K A180619 nonn %O A180619 0,1 %A A180619 _Ben Branman_, Sep 12 2010