A197000 - OEIS

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A197000

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=1+cos(x) orthogonally.

1, 2, 4, 8, 8, 0, 1, 4, 3, 6, 7, 2, 1, 5, 5, 0, 8, 5, 6, 0, 4, 7, 5, 1, 2, 5, 0, 2, 0, 1, 2, 8, 3, 8, 1, 5, 3, 5, 5, 8, 7, 6, 1, 4, 3, 0, 3, 6, 0, 8, 2, 1, 6, 3, 4, 1, 4, 6, 0, 2, 5, 0, 2, 0, 4, 4, 2, 0, 8, 5, 0, 0, 0, 1, 4, 5, 2, 7, 2, 5, 5, 3, 7, 0, 6, 7, 4, 7, 9, 9, 7, 6, 6, 0, 1, 4, 2, 5, 9, 6

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

See the Mathematica program for a graph.

xo=1.2488014367215508560475125020128381535587614...

yo=1.3164595537507515212878992732671186100622603...

m=1.05417844265684217515747734305673483746142104...

|OP|=1.81454423617045980814297669595599066552030...

LINKS

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

MATHEMATICA

c = 1;

xo = x /.

FindRoot[x == Sin[x] (c + Cos[x]), {x, 1, 1.3}, WorkingPrecision -> 100]

RealDigits[xo] (* A197000 *)

m = 1/Sin[xo]

RealDigits[m] (* A197001 *)

yo = m*xo

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

Show[Plot[{c + Cos[c*x], yo - (1/m) (x - xo)}, {x, 0, Pi}], ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 2}], PlotRange -> All, AspectRatio -> Automatic, AxesOrigin -> Automatic]

CROSSREFS

Cf. A197001, A196996, A197002.

Sequence in context: A261298 A133007 A141532 * A198428 A365251 A357159

Adjacent sequences: A196997 A196998 A196999 * A197001 A197002 A197003

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 09 2011

STATUS

approved