A196831 Decimal expansion of the number x satisfying 0 < x < 2*Pi and x^2 + 2*x*tan(x) + 1 = 0.

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

Offset: 1

Author

Clark Kimberling, Oct 07 2011

Keywords

• nonn
• cons

Examples

			x=2.214416905079636330679565960367792215966376475...
		

Crossrefs

Cf. A196825, A196832.

Programs

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 *)