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A197003 Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+pi/4) orthogonally over the interval [0,2*pi] (as in A197002). 2
1, 0, 9, 3, 1, 6, 9, 7, 4, 4, 9, 8, 5, 0, 1, 6, 9, 2, 2, 0, 8, 8, 1, 5, 3, 2, 1, 4, 1, 6, 0, 5, 7, 9, 7, 1, 4, 4, 0, 4, 8, 9, 0, 6, 5, 9, 2, 9, 4, 8, 9, 8, 8, 8, 3, 5, 6, 3, 5, 1, 7, 5, 1, 3, 3, 2, 4, 9, 6, 0, 5, 3, 7, 6, 7, 0, 9, 4, 4, 7, 3, 6, 8, 3, 7, 6, 7, 0, 6, 7, 9, 9, 3, 4, 8, 1, 7, 9, 3, 4, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See the Mathematica program for a graph.

xo=0.3695425666075803208276560438369...

yo=0.4039727532995172093189617400663...

m=1.09316974498501692208815321416057...

|OP|=0.54749949218543621432520415035...

LINKS

Table of n, a(n) for n=1..101.

MATHEMATICA

c = Pi/4;

xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]

RealDigits[xo] (* A197002 *)

m = 1/Sin[xo + c]

RealDigits[m]  (* A197003 *)

yo = m*xo

d = Sqrt[xo^2 + yo^2]

Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, 1}], ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All, AspectRatio -> Automatic, AxesOrigin -> Automatic]

CROSSREFS

Cf. A197002, A196996, A197000.

Sequence in context: A187832 A085579 A081813 * A048799 A309893 A188887

Adjacent sequences:  A197000 A197001 A197002 * A197004 A197005 A197006

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 09 2011

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)