%I #7 Mar 30 2012 18:57:50
%S 9,3,5,0,2,7,2,8,8,4,7,4,9,6,7,8,3,6,1,4,5,1,9,4,4,2,7,5,3,2,3,9,7,7,
%T 6,3,1,7,5,1,8,3,5,1,0,0,5,2,6,8,3,9,0,8,9,5,3,4,7,2,9,7,9,7,0,1,2,8,
%U 5,7,1,3,0,3,2,2,9,6,3,6,0,2,7,4,7,3,1,0,4,9,2,9,1,6,2,8,9,9,9,4
%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(3x) orthogonally.
%C See the Mathematica program for a graph.
%C xo=0.9350272884749678361451944275323...
%C yo=0.3301955980451199836007253971727...
%C m=0.35314006565912096755666111412785...
%C |OP|=0.99161744799152518925689622748...
%t c = 3;
%t xo = x /. FindRoot[0 == x + c*Sin[c*x] Cos[c*x], {x, .8, 1.2}, WorkingPrecision -> 100]
%t RealDigits[xo] (* A196996 *)
%t m = Sin[c*xo]/xo
%t RealDigits[m] (* A196997 *)
%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}], ContourPlot[{y == m*x}, {x, 0, 1.5}, {y, -.1, 1}], PlotRange -> All, AspectRatio -> Automatic]
%Y Cf. A196997, A197000, A197002.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 09 2011