A196915 Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/(1+x^2) and y=c*cos(x), where c is given by A196914.

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

Offset

0,1

Links

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

Example

-0.60762223769686865859001002682026364322748...

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 *)

Prog

(PARI) t=solve(x=.5, 1, tan(x)*(x^2+1)- 2*x); -sin(t)*sqrt(t^4 + 6*t^2 + 1)/(t^4 + 2*t^2 + 1) \\ Charles R Greathouse IV, Apr 24 2026

Crossrefs

Cf. A196914, A196913.

Sequence in context: A341906 A365163 A195432 * A374407 A249651 A021626

Adjacent sequences: A196912 A196913 A196914 * A196916 A196917 A196918

Keyword

nonn,cons

Author

Clark Kimberling, Oct 07 2011

Status

approved