A196913 Decimal expansion of the number x satisfying 0 < x < 2*Pi and 2x = (1 + x^2)*tan(x).

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

Offset

0,1

Links

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

Example

0.7682171553153782504312122866979254095466915658...

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) solve(x=.5, 1, tan(x)*(x^2+1)- 2*x) \\ Charles R Greathouse IV, Apr 24 2026

Crossrefs

Cf. A196816, A196914.

Sequence in context: A195370 A277077 A381456 * A091343 A196397 A238301

Adjacent sequences: A196910 A196911 A196912 * A196914 A196915 A196916

Keyword

nonn,cons

Author

Clark Kimberling, Oct 07 2011

Status

approved