

A196998


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.


2



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, 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, 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
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OFFSET

1,3


COMMENTS

See the Mathematica program for a graph.
xo=1.055537135075475249854148417892290354122...
yo=0.481836913462240473673427172075977637742...
m=0.4564850420234501281397606474354137170643...
OP=1.1603126538559168441096914160911620183...


LINKS

Table of n, a(n) for n=1..100.


MATHEMATICA

c = 5/2;
xo = x /. FindRoot[0 == x + c*Sin[c*x] Cos[c*x], {x, .8, 1.2}, WorkingPrecision > 100]
RealDigits[xo] (* A196998 *)
m = Sin[c*xo]/xo
RealDigits[m] (* A196999 *)
yo = m*xo
d = Sqrt[xo^2 + yo^2]
Show[Plot[{Sin[c*x], yo  (1/m) (x  xo)}, {x, 0, Pi/c}],
ContourPlot[{y == m*x}, {x, 0, Pi/c}, {y, .1, 1}], PlotRange > All, AspectRatio > Automatic]


CROSSREFS

Cf. A196996, A197000, A197002.
Sequence in context: A054245 A302552 A193887 * A232614 A254609 A133707
Adjacent sequences: A196995 A196996 A196997 * A196999 A197000 A197001


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 09 2011


STATUS

approved



