A196774 Decimal expansion of the number c for which the curve y=c+1/x is tangent to the curve y=sin(x), and 0 < x < 2*Pi.

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

Offset: 0

Author

Clark Kimberling, Oct 06 2011

Keywords

• nonn
• cons

Examples

			x=0.4208427526566741951606531250693278249070426065...
		

Crossrefs

Cf. A196773, A196775.

Programs

Mathematica

Plot[{1/x + .42, Sin[x]}, {x, 0, 2 Pi}]
t = x /. FindRoot[-1 == (x^2) Cos[x], {x, 1.5, 2.5}, WorkingPrecision -> 100]
RealDigits[t]    (* A196773 *)
c = N[-1/t + Sin[t], 100]
RealDigits[c]    (* A196774 *)
slope = N[-1/t^2, 100]
RealDigits[slope](* A196775 *)