A290931 Radius of a circle enclosing three mutually tangent circles, such that they have coprime integer radii and with collectively six distinct points of tangency.
6, 6, 15, 18, 20, 21, 28, 35, 40, 40, 42, 42, 45, 45, 52, 54, 56, 63, 66, 66, 72, 75, 77, 88, 91, 95, 99, 100, 104, 105, 105, 110, 112, 117, 120, 126, 130, 143, 153, 153, 156, 160, 160, 165, 165, 168, 170, 175, 186, 187, 189, 190, 195, 196, 198, 198, 204, 208, 208
Offset: 1
Keywords
Examples
The table gives the first 8 examples: a b c d == == == == 6 3 2 1 6 3 3 2 15 10 3 2 18 9 8 8 20 12 5 3 21 14 7 6 28 21 4 3 35 15 14 6
Links
- Ray Chandler, Table of n, a(n) for n = 1..837
- Eric Weisstein's World of Mathematics, Soddy Circles.
- Eric Weisstein's World of Mathematics, Tangent Circles
- Wikipedia, Descartes' theorem
Crossrefs
Cf. A290508 (4 circles tangent externally).
Programs
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Mathematica
aMax = 150; (* WARNING: O(n^3) *) Do[ If[x \[NotElement] Rationals, Continue[]]; {d1, d2} = 1/(-(1/a) + 1/b + 1/c + {1, -1} 2 x); If[GCD[a, b, c, d1] == 1, {a, b, c, d1} // Sow]; If[d2 > c || d2 == d1, Continue[]]; If[GCD[a, b, c, d2] == 1, {a, b, c, d2} // Sow]; , {a, aMax}, {b, 2, a - 2}, {c, Min[b, a - b]} , {x, {Sqrt[(-a + b + c)/(-a b c)]}}] // Reap // Last // Last // TableForm
Extensions
Description clarified by Ray Chandler, Aug 19 2017
Comments