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 A197029 Decimal expansion of the radius of the smallest circle tangent to the x axis and to the curve y=-cos(4x) at points (x,y), (-x,y). 1
 5, 0, 6, 0, 6, 4, 3, 3, 3, 2, 1, 6, 5, 2, 4, 5, 1, 0, 0, 5, 4, 6, 3, 7, 6, 2, 1, 7, 7, 3, 4, 7, 1, 4, 4, 1, 1, 6, 9, 4, 8, 7, 3, 8, 8, 6, 1, 8, 3, 2, 2, 7, 7, 3, 2, 8, 6, 6, 4, 0, 3, 6, 7, 1, 7, 8, 8, 6, 3, 1, 4, 2, 1, 9, 5, 5, 2, 2, 8, 4, 0, 9, 3, 3, 8, 4, 7, 3, 0, 0, 8, 5, 2, 6, 1, 4, 6, 0, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Let (x,y) denote the point of tangency, where x>0: x=0.488618197079923270050681129865078039260837... y=0.374332154777652501331094642913853652491893... slope=3.709178750935618333987343550424591912283... (The Mathematica program includes a graph.) LINKS EXAMPLE radius=0.5060643332165245100546376217734714411... MATHEMATICA r = .5; c = 4; Show[Plot[-Cos[c*x], {x, -1, 1}], ContourPlot[x^2 + (y - r)^2 == r^2, {x, -1, 1}, {y, -1.5, 2}], PlotRange -> All, AspectRatio -> Automatic] u[x_] := -Cos[c*x] + x/(c*Sin[c*x]); t1 = x /. FindRoot[Sqrt[u[x]^2 - x^2] == u[x] + Cos[c*x], {x, .4, .5}, WorkingPrecision -> 100] t = Re[t1]    (* x coordinate of tangency point *) y = -Cos[c*t] (* y coordinate of tangency point *) radius = u[t] RealDigits[radius] (* A197029 *) slope = c*Sin[c*t] (* slope at tangency point *) CROSSREFS Cf. A197026, A196027, A196028, A196022. Sequence in context: A021668 A004552 A130415 * A197030 A035550 A197508 Adjacent sequences:  A197026 A197027 A197028 * A197030 A197031 A197032 KEYWORD nonn,cons AUTHOR Clark Kimberling, Oct 09 2011 STATUS approved

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Last modified September 27 04:10 EDT 2021. Contains 347673 sequences. (Running on oeis4.)