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A197028 Decimal expansion of the radius of the smallest circle tangent to the x axis and to the curve y=-cos(3x) at points (x,y), (-x,y). 1
7, 3, 6, 6, 0, 6, 6, 3, 4, 1, 4, 7, 1, 5, 1, 8, 2, 4, 9, 9, 2, 0, 7, 8, 9, 0, 5, 0, 8, 2, 4, 5, 2, 0, 6, 4, 8, 2, 2, 7, 6, 0, 6, 3, 9, 9, 8, 3, 9, 0, 2, 7, 9, 1, 5, 0, 8, 1, 4, 8, 0, 8, 0, 6, 8, 3, 6, 8, 0, 1, 0, 5, 1, 2, 3, 8, 5, 3, 9, 8, 9, 0, 6, 3, 9, 4, 3, 6, 5, 7, 3, 0, 8, 0, 0, 9, 2, 6, 2 (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=0.6888117352645178597708892254141829843113...

y=0.4755937478149254230061087613442876576146...

slope=2.6389951275730271940627334805152084806...

(The Mathematica program includes a graph.)

LINKS

Table of n, a(n) for n=0..98.

EXAMPLE

radius=0.7366066341471518249920789050824520648...

MATHEMATICA

r = .737; c = 3;

Show[Plot[-Cos[c*x], {x, -2, 2}],

ContourPlot[x^2 + (y - r)^2 == r^2, {x, -3, 3}, {y, -1.5, 3}], 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, .6, .8}, WorkingPrecision -> 100]

t = Re[t1];

RealDigits[t]  (* x coordinate of tangency point *)

y = -Cos[c*t]  (* y coordinate of tangency point *)

radius = u[t]

RealDigits[radius] (* A197028 *)

slope = c*Sin[c*t] (* slope at tangency point *)

CROSSREFS

Cf. A197026, A196027, A196029, A196021.

Sequence in context: A238695 A019819 A215693 * A257819 A182111 A023643

Adjacent sequences:  A197025 A197026 A197027 * A197029 A197030 A197031

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 09 2011

STATUS

approved

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)