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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
5, 9, 17, 36, 39, 64, 74, 81, 100 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 14 08:33 EDT 2020. Contains 335720 sequences. (Running on oeis4.)