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 A102302 #30 Feb 16 2025 08:32:55
%S A102302 3,3,4,3,5,5,6,5,7,7,8,7,9,9,10,9,11,11,12,11,13,13,14,13,15,15,16,15,
%T A102302 17,17,18,17,19,19,20,19,21,21,22,21,23,23,24,23,25,25,26,25,27,27,28,
%U A102302 27,29,29,30,29,31,31,32,31,33,33,34,33,35,35,36,35,37,37,38,37,39,39
%N A102302 Largest number < n/2 coprime to n.
%C A102302 The densest possible star-shaped regular n-gon is formed by connecting with straight lines every a(n)-th point out of n regularly spaced points lying on a circumference.
%C A102302 For a given n there are A055684(n) different star-shaped regular polygons. The minimum skip increment for connecting points on the circumference is given by A053669(n), the maximum skip increment is given by a(n). There are no star-shaped polygons for n=3,4,6 and unique star-shaped polygons for n=5,8,10 and 12, for which a(n) = A053669(n).
%H A102302 Colin Barker, <a href="/A102302/b102302.txt">Table of n, a(n) for n = 7..1000</a>
%H A102302 Jay Kappraff, Gary W. Adamson, <a href="http://archive.bridgesmathart.org/2001/bridges2001-67.pdf">Polygons and Chaos</a>, BRIDGES Mathematical Connections in Art, Music, and Science, 2001.
%H A102302 Hugo Pfoertner, <a href="/A055684/a055684.pdf">Star-shaped regular polygons.</a>
%H A102302 Hugo Pfoertner, <a href="/A102302/a102302.pdf">(Star-Shaped-) Polygons with Maximal Density.</a>
%H A102302 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StarPolygon.html">Star Polygon.</a>
%H A102302 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A102302 a(4*k-1) = a(4*k) = a(4*k+2) = 2*k-1; a(4*k+1) = 2*k.
%F A102302 a(n) = (1/2) (n - (I^n + (-I)^n)/2 - (-1)^n + 4). - _Ralf Stephan_, May 17 2007
%F A102302 a(n) = a(n-1)+a(n-4)-a(n-5) for n>11. - _Colin Barker_, Feb 21 2015
%F A102302 G.f.: -x^7*(x^4+x^3-x^2-3) / ((x-1)^2*(x+1)*(x^2+1)). - _Colin Barker_, Feb 21 2015
%t A102302 lnc[n_]:=Module[{k=Floor[n/2]},While[!CoprimeQ[n,k],k--];k]; Array[ lnc,90,7] (* _Harvey P. Dale_, May 15 2021 *)
%o A102302 (PARI) Vec(-x^7*(x^4+x^3-x^2-3)/((x-1)^2*(x+1)*(x^2+1)) + O(x^100)) \\ _Colin Barker_, Feb 21 2015
%Y A102302 Cf. A053669 (least number coprime to n), A055684 (number of different n-pointed stars).
%K A102302 easy,nonn
%O A102302 7,1
%A A102302 _Hugo Pfoertner_, Jan 23 2005