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 A062536 #16 Feb 16 2025 08:32:44
%S A062536 5,9,17,36,39,64,74,81,100
%N A062536 Increasing values for the radius of the inner Soddy circle associated with three unequal kissing circles, the four radii of the system forming a primitive quadruple.
%C A062536 A family of nonsquare values for a(n) may be generated by the formula a(n) = n{(n + 2)^2 + 1 }/2 for n not a multiple of 5. For some values of a(n) which are squares, the three kissing circles share a common external tangent and their radii are related by 1/sqrt(x) = 1/sqrt(y) + 1/sqrt(z).
%H A062536 Pat Ballew, <a href="http://www.pballew.net/soddy.html">Soddy's Formula</a>
%H A062536 Thesaurus.maths.org, <a href="http://thesaurus.maths.org/dictionary/map/word/2105">Soddy's Formula or Descartes' Circle Theorem</a>
%H A062536 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SoddyCircles.html">Soddy Circles.</a>
%F A062536 The inner Soddy circle radius r is explicitly given by 1/r = 1/x + 1/y + 1/z + 2/R with R^2 = xyz/(x + y +z) where x, y, z are the kissing circles' radii and R the radius of the circle orthogonal to the latter three.
%e A062536 The quadruples (9,28,63,252) and (74,312,481,888) for instance are respectively the 2nd and 7th primitive solution set (r,x,y,z) satisfying the given explicit formula for r.
%K A062536 more,nonn
%O A062536 1,1
%A A062536 _Lekraj Beedassy_, Jun 25 2001