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.

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

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