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 A259442 #14 Jul 15 2015 17:51:00
%S A259442 4,11,33,102,322,1017,3215,10167,32149,101664,321488,1016633,3214876,
%T A259442 10166330,32148757,101663296,321487567,1016632951,3214875668,
%U A259442 10166329505,32148756680,101663295049,321487566791,1016632950485,3214875667907,10166329504841,32148756679070,101663295048410
%N A259442 a(n) is the least number of sides of a regular circumscribed k-gon whose perimeter yields Pi to within 1/10^n.
%C A259442 Since the perimeter equals n*tan(180ยบ/n), increasing n to greater values will yield a more accurate value of Pi.
%C A259442 Lim n -> inf., a(n+1)/a(n) = sqrt(10). This implies that a(n+2) ~ 10*a(n).
%C A259442 Lim n -> inf., a(2n) = 10^n*sqrt(Pi^3/3) and a(2n+1) = 10^n*sqrt(Pi^3/30).
%C A259442 Lim n -> inf., a(n)/A259441(n) = sqrt(2).
%D A259442 William H. Beyer, Ed., CRC Standard Mathematical Tables, 27th Ed., IV - Geometry, Mensuration Formulas, p. 122, Boca Raton 1984.
%D A259442 Daniel Zwillinger, Editor-in-Chief, 31st Ed., CRC Standard Mathematical Tables and Formulae, 4.5.3 Geometry - Regular Polygons, p. 324, Boca Raton, 2003.
%D A259442 Jan Gullberg, Mathematics: From the Birth of Numbers, 13.3 Solving Triangles, p. 479, W. W. Norton & Co., NY, 1997.
%D A259442 Catherine A. Gorini, Ph.D., The Facts on File Geometry Handbook, Charts & Tables, p. 262, Checkmark Books, NY, 2005.
%H A259442 mathematicsonline, <a href="https://www.youtube.com/watch?v=DLZMZ-CT7YU/"> How to Calculate Pi using Archimedes' Method</a>
%e A259442 a(0) # 3 since the perimeter of the circumscribed triangle is sqrt(27) which equals approximately 5.196152... which exceeds Pi by more than 1;
%e A259442 a(0) = 4 since the perimeter of the circumscribed square is 4 and this is within 1 of the true value of Pi;
%e A259442 a(1) = 11 since the perimeter of the circumscribed 11-gon which equals approximately 3.229891... which is within 0.1 of the true value of Pi;
%e A259442 a(2) = 33 since the perimeter of the circumscribed 33-gon which equals approximately 3.151117... which is within 0.01 of the true value of Pi; etc.
%t A259442 f[n_] := Block[{k = Floor[ Sqrt[ 10]*f[n - 1]] - 6}, While[Pi + 10^-n < k*Tan[Pi/k], k++]; k]; f[-1] = 3; Array[f, 28, 0]
%Y A259442 Cf. A000796, A244644, A259441.
%K A259442 easy,nonn
%O A259442 0,1
%A A259442 _Robert G. Wilson v_, Jun 27 2015