

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.


3




OFFSET

1,1


COMMENTS

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).


LINKS

Table of n, a(n) for n=1..9.
Pat Ballew, Soddy's Formula
Thesaurus.maths.org, Soddy's Formula or Descartes' Circle Theorem
Eric Weisstein's World of Mathematics, Soddy Circles.


FORMULA

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.


EXAMPLE

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.


CROSSREFS

Sequence in context: A020737 A262452 A147401 * A324718 A099213 A146067
Adjacent sequences: A062533 A062534 A062535 * A062537 A062538 A062539


KEYWORD

more,nonn


AUTHOR

Lekraj Beedassy, Jun 25 2001


STATUS

approved



