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 A253570 #27 Mar 14 2015 03:40:33 %S A253570 0,1,1,1,3,4,5,7,8,9 %N A253570 Maximum number of circles of radius 1 that can be packed into a regular n-gon with side length 2 (conjectured). %C A253570 The values were obtained by constructing the circle arrangements in a vector graphics program and have not been proved to be correct. %C A253570 From _David Consiglio, Jr._, Jan 09 2015: (Start) %C A253570 As n increases, the n-gon more and more closely approximates a circle. As a result, the lower bound (which is highly likely to be the correct term for larger and larger n) is the number of circles that can be packed into an inscribed circle, the radius of which is given by the expression cot(Pi/n). Look up this radius in column 3 at www.packomania.com to find the lower bound of a(n). %C A253570 A rough upper bound would be the closest packing of circles into the area of the n-gon (formula below). A better upper bound is likely possible. %C A253570 See file for lower and upper bounds through a(20). The lower bounds have been proved for a(3) through a(13). %C A253570 (End) %H A253570 David Consiglio, Jr., <a href="/A253570/a253570.txt">Lower and Upper Bounds</a> %H A253570 Felix Fröhlich, <a href="/A253570/a253570.svg">Illustration of circle arrangements associated with a(3)-a(12)</a> %H A253570 E. Specht, <a href="http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html">The best known packings of equal circles in a circle (complete up to N = 2600)</a>, Packomania. %F A253570 Upper bound = floor(n/(2*sqrt(3)*tan(Pi/n))). %Y A253570 Cf. A023393, A051657, A084616. %K A253570 nonn,hard,more %O A253570 3,5 %A A253570 _Felix Fröhlich_, Jan 03 2015