A196833 Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/(1+x^2) and y=c*sin(x), where c is given by A196832.

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

Offset

0,2

Links

Table of n, a(n) for n=0..99.

Example

x=-0.12707184118644190594794464339300176838562544...

Mathematica

Plot[{1/(1 + x^2), .205 Sin[x]}, {x, 0, Pi}]
t = x /. FindRoot[x^2 + 2 x*Tan[x] + 1 == 0, {x, 2, 3}, WorkingPrecision -> 100]
RealDigits[t]     (* A196831 *)
c = N[Csc[t]/(1 + t^2), 100]
RealDigits[c]     (* A196832 *)
slope = N[c*Cos[t], 100]
RealDigits[slope] (* A196833 *)

Crossrefs

Cf. A196825, A196832.

Sequence in context: A021791 A325905 A199273 * A245224 A016638 A199398

Adjacent sequences: A196830 A196831 A196832 * A196834 A196835 A196836

Keyword

nonn,cons

Author

Clark Kimberling, Oct 07 2011

Status

approved