The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A197023 Decimal expansion of the radius of the circle tangent to the curve y=1/(1+x^2) and to the positive x and y axes. 3
 3, 9, 5, 8, 6, 2, 4, 3, 7, 8, 4, 7, 4, 8, 0, 7, 9, 8, 2, 4, 0, 7, 0, 7, 7, 2, 2, 5, 6, 6, 3, 1, 5, 5, 2, 7, 3, 3, 4, 3, 4, 3, 9, 2, 9, 2, 4, 9, 1, 0, 0, 0, 8, 2, 5, 0, 4, 4, 2, 7, 9, 6, 3, 2, 5, 1, 2, 6, 4, 4, 3, 7, 9, 1, 1, 1, 8, 8, 1, 3, 0, 8, 6, 6, 5, 3, 8, 4, 8, 9, 0, 0, 5, 9, 1, 5, 8, 3, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Let (x,y) denote the point of tangency. Then x=0.611116305530271280094961817959748153764566... y=0.728086522083031555694579423798015759485165... slope=-0.64791770945231344102369199673001177755... (The Mathematica program includes a graph.) LINKS Table of n, a(n) for n=0..98. EXAMPLE radius=0.39586243784748079824070772256631552733434... MATHEMATICA r = .396; c = 1; Show[Plot[c/(1 + x^2), {x, 0, 1.5}], ContourPlot[(x - r)^2 + (y - r)^2 == r^2, {x, -1, 1}, {y, -1, 1}], PlotRange -> All, AspectRatio -> Automatic, AxesOrigin -> Automatic] u[x_] := (x*(1 + x^2)^3 - 2*x*c^2)/((1 + x^2)^3 - 2*c*x*(1 + x^2)) v = x /. FindRoot[c/(1 + x^2) == u[x] + Sqrt[2*u[x]*x - x^2], {x, .4, 1}, WorkingPrecision -> 100] t = Re[v] ; RealDigits[t] (* x coord. of tangency pt. *) y = c/(1 + t^2) (* y coord. of tangency pt. *) radius = u[t] RealDigits[radius] (* A197023 *) slope = -2*c*t/(1 + t^2)^2 (* slope at tangency point *) CROSSREFS Cf. A197020, A197024, A197025, A197016. Sequence in context: A332564 A199053 A200595 * A096418 A100811 A223652 Adjacent sequences: A197020 A197021 A197022 * A197024 A197025 A197026 KEYWORD nonn,cons AUTHOR Clark Kimberling, Oct 08 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 12:36 EDT 2024. Contains 372913 sequences. (Running on oeis4.)