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 A197006 Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) in which a line y=mx meets the curve y=cos(x+pi/6) orthogonally. 3
 4, 6, 0, 8, 8, 5, 5, 8, 0, 8, 6, 0, 9, 6, 5, 9, 7, 6, 9, 8, 7, 9, 8, 1, 2, 8, 2, 5, 1, 3, 6, 9, 8, 2, 7, 7, 2, 4, 3, 7, 4, 9, 9, 9, 8, 7, 4, 3, 9, 3, 4, 3, 5, 6, 9, 3, 2, 5, 7, 8, 4, 3, 3, 9, 2, 4, 8, 3, 4, 7, 5, 2, 2, 8, 8, 0, 3, 8, 7, 9, 7, 1, 3, 0, 5, 0, 5, 9, 7, 4, 8, 0, 7, 6, 7, 9, 4, 3, 8, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS See the Mathematica program for a graph. xo=0.460885580860965976987981282513698... yo=0.553292712300593256734925495541442... m=1.2004990723879979061250465124427113... |OP|=0.7201030093885853693640956082816... LINKS MATHEMATICA c = Pi/6; xo = x /.  FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100] RealDigits[xo] (* A197006 *) m = 1/Sin[xo + c] RealDigits[m] (* A197007 *) yo = m*xo d = Sqrt[xo^2 + yo^2] Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, Pi/2}], ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All, AspectRatio -> Automatic, AxesOrigin -> Automatic] CROSSREFS Cf. A197007, A197002, A196996, A197000. Sequence in context: A198228 A200349 A021221 * A224273 A111828 A013249 Adjacent sequences:  A197003 A197004 A197005 * A197007 A197008 A197009 KEYWORD nonn,cons AUTHOR Clark Kimberling, Oct 10 2011 STATUS approved

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