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.

69, 70, 132, 138, 140, 153, 198, 207, 210, 216, 238, 252, 264, 264, 264, 270, 276, 280, 285, 290, 306, 345, 350, 390, 396, 396, 414, 420, 429, 432, 459, 476, 483, 490, 504, 504, 520, 528, 528, 528, 539, 540, 552, 560, 567, 570, 580, 594, 595, 612, 621, 630

Offset: 1

Author

Colin Barker, Apr 08 2015

Keywords

• nonn

Links

• Kival Ngaokrajang, Illustration of the first three solutions
• Eric Weisstein's World of Mathematics, Soddy Circles.

Crossrefs

See also the many sequences arising from Apollonian circle packing: A135849, A137246, A154636, etc.

Also the sequences related to Soddy's circle packings: A046159, A046160, A062536, etc.

Programs

PARI

soddy(k) = {
  s=[];
  for(a=1, k,
    for(b=1, a-1,
      for(c=1, b-1,
        if(issquare(a*b*c*(a+b+c), &t),
          if(a*b*c % (a*b+a*c+b*c+2*t) == 0,
            s=concat(s, a)
          )
        )
      )
    )
  );
  s
}
soddy(500)