A196832 Decimal expansion of the number c for which the curve y=1/(1+x^2) is tangent to the curve y=c*sin(x), and 0 < x < 2*Pi.

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

Offset

0,1

Links

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

Example

c=0.21175267284313356422891828878302637078159516791...

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 *)

Prog

(PARI) t=solve(x=2, 3, x^2 + 2*x*tan(x) + 1); 1/sin(t)/(1 + t^2) \\ Charles R Greathouse IV, Feb 22 2025

Crossrefs

Cf. A196825.

Sequence in context: A169730 A220725 A333142 * A005450 A039760 A156882

Adjacent sequences: A196829 A196830 A196831 * A196833 A196834 A196835

Keyword

nonn,cons

Author

Clark Kimberling, Oct 07 2011

Status

approved