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A196999 Decimal expansion of slope of the line y=mx which meets the curve y=cos(5x/2) orthogonally (as in A196998). 2
4, 5, 6, 4, 8, 5, 0, 4, 2, 0, 2, 3, 4, 5, 0, 1, 2, 8, 1, 3, 9, 7, 6, 0, 6, 4, 7, 4, 3, 5, 4, 1, 3, 7, 1, 7, 0, 6, 4, 3, 0, 5, 0, 9, 2, 7, 8, 2, 9, 2, 8, 5, 3, 8, 2, 3, 5, 8, 0, 0, 3, 1, 8, 0, 1, 9, 6, 2, 6, 6, 6, 0, 4, 8, 0, 0, 6, 8, 5, 3, 6, 2, 8, 1, 6, 8, 7, 0, 7, 7, 1, 2, 8, 6, 7, 3, 1, 0, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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=0..98.

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, A196997, A197000, A197002.

Sequence in context: A096291 A201933 A016719 * A090370 A002129 A113184

Adjacent sequences:  A196996 A196997 A196998 * A197000 A197001 A197002

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 09 2011

STATUS

approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)