login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 09:21 EST 2019. Contains 329877 sequences. (Running on oeis4.)