%I #5 Mar 30 2012 18:57:50
%S 1,0,5,5,5,3,7,1,3,5,0,7,5,4,7,5,2,4,9,8,5,4,1,4,8,4,1,7,8,9,2,2,9,0,
%T 3,5,4,1,2,2,2,7,9,8,0,6,9,6,2,7,3,2,9,7,3,0,4,0,0,8,2,4,1,7,5,4,1,5,
%U 4,5,5,4,2,8,0,0,9,4,4,9,3,6,6,6,9,4,4,5,9,1,5,5,0,4,5,7,4,7,1,5
%N Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) at which a line y=m*x meets the curve y=cos(5x/2) orthogonally.
%C See the Mathematica program for a graph.
%C xo=1.055537135075475249854148417892290354122...
%C yo=0.481836913462240473673427172075977637742...
%C m=0.4564850420234501281397606474354137170643...
%C |OP|=1.1603126538559168441096914160911620183...
%t c = 5/2;
%t xo = x /. FindRoot[0 == x + c*Sin[c*x] Cos[c*x], {x, .8, 1.2}, WorkingPrecision -> 100]
%t RealDigits[xo] (* A196998 *)
%t m = Sin[c*xo]/xo
%t RealDigits[m] (* A196999 *)
%t yo = m*xo
%t d = Sqrt[xo^2 + yo^2]
%t Show[Plot[{Sin[c*x], yo - (1/m) (x - xo)}, {x, 0, Pi/c}],
%t ContourPlot[{y == m*x}, {x, 0, Pi/c}, {y, -.1, 1}], PlotRange -> All, AspectRatio -> Automatic]
%Y Cf. A196996, A197000, A197002.
%K nonn,cons
%O 1,3
%A _Clark Kimberling_, Oct 09 2011