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A256694 The radius of the largest of four circles with different integer radii arranged so that each circle is tangent externally to the other three circles.

%I A256694 #12 Feb 16 2025 08:33:25
%S A256694 69,70,132,138,140,153,198,207,210,216,238,252,264,264,264,270,276,
%T A256694 280,285,290,306,345,350,390,396,396,414,420,429,432,459,476,483,490,
%U A256694 504,504,520,528,528,528,539,540,552,560,567,570,580,594,595,612,621,630
%N A256694 The radius of the largest of four circles with different integer radii arranged so that each circle is tangent externally to the other three circles.
%H A256694 Kival Ngaokrajang, <a href="/A256694/a256694.pdf">Illustration of the first three solutions</a>
%H A256694 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SoddyCircles.html">Soddy Circles.</a>
%o A256694 (PARI)
%o A256694 soddy(k) = {
%o A256694   s=[];
%o A256694   for(a=1, k,
%o A256694     for(b=1, a-1,
%o A256694       for(c=1, b-1,
%o A256694         if(issquare(a*b*c*(a+b+c), &t),
%o A256694           if(a*b*c % (a*b+a*c+b*c+2*t) == 0,
%o A256694             s=concat(s, a)
%o A256694           )
%o A256694         )
%o A256694       )
%o A256694     )
%o A256694   );
%o A256694   s
%o A256694 }
%o A256694 soddy(500)
%Y A256694 See also the many sequences arising from Apollonian circle packing: A135849, A137246, A154636, etc.
%Y A256694 Also the sequences related to Soddy's circle packings: A046159, A046160, A062536, etc.
%K A256694 nonn
%O A256694 1,1
%A A256694 _Colin Barker_, Apr 08 2015