A196914 Decimal expansion of the number c for which the curve y=1/(1+x^2) is tangent to the curve y=c*cos(x), and 0 < x < 2*Pi.

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

Offset

0,1

Links

Table of n, a(n) for n=0..98.

Formula

x=0.87446003662400926554814644840673725663073...

Example

c=0.87446003662400926554814644840673725663073...

Mathematica

Plot[{1/(1 + x^2), 0.874*Cos[x]}, {x, .5, 1}]
t = x /. FindRoot[Tan[x] == 2 x/(1 + x^2), {x, .5, 1}, WorkingPrecision -> 100]
RealDigits[t]    (* A196913 *)
c = N[Sqrt[t^4 + 6 t^2 + 1]/(t^4 + 2 t^2 + 1), 100]
RealDigits[c]    (* A196914 *)
slope = N[-c*Sin[t], 100]
RealDigits[slope](* A196915 *)

Crossrefs

Cf. A196913, A196915.

Sequence in context: A268046 A260060 A260800 * A072102 A274442 A249136

Adjacent sequences: A196911 A196912 A196913 * A196915 A196916 A196917

Keyword

nonn,cons

Author

Clark Kimberling, Oct 07 2011

Status

approved