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A197002 Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) in which a line y=mx meets the curve y=cos(x+pi/4) orthogonally. 15
3, 6, 9, 5, 4, 2, 5, 6, 6, 6, 0, 7, 5, 8, 0, 3, 2, 0, 8, 2, 7, 6, 5, 6, 0, 4, 3, 8, 3, 6, 9, 3, 6, 7, 0, 2, 0, 0, 6, 7, 0, 5, 8, 7, 9, 4, 5, 0, 3, 7, 8, 7, 3, 2, 4, 8, 2, 8, 4, 0, 3, 1, 7, 8, 8, 6, 6, 4, 2, 3, 2, 7, 4, 4, 1, 7, 7, 3, 7, 9, 7, 2, 9, 9, 6, 8, 8, 0, 5, 3, 4, 6, 5, 8, 8, 3, 2, 6, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See the Mathematica program for a graph.

xo=0.36954256660758032082765604383693...

yo=0.40397275329951720931896174006631...

m=1.093169744985016922088153214160579...

|OP|=0.547499492185436214325204150357...

LINKS

Table of n, a(n) for n=0..99.

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. A197003, A196996, A197000.

Sequence in context: A300714 A020850 A163341 * A227929 A019700 A151862

Adjacent sequences:  A196999 A197000 A197001 * A197003 A197004 A197005

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 09 2011

STATUS

approved

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Last modified February 24 00:51 EST 2020. Contains 332195 sequences. (Running on oeis4.)