A196765 Decimal expansion of the positive number c for which the curve y=c/x is tangent to the curve y=sin(x), and 0 < x < 2*Pi.

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

Offset: 1

Author

Clark Kimberling, Oct 06 2011

Keywords

• nonn
• cons

Comments

Also, the least local maximum of x*sin(x), which occurs exactly at x = +-A196504, where x = +A196504 is the x-coordinate of this point of tangency of c/x and sin(x) in the first quadrant. There also exists a negative constant d such that d/x and sin(x) are tangent in the fourth quadrant for 0 < x < 2*Pi. - Rick L. Shepherd, Jan 12 2014

Examples

			x=1.8197057411596530462069576803755281456165224784...
		

Crossrefs

Cf. A196760.

Programs

Mathematica

Plot[{Sin[x], 1/x, 1.82/x}, {x, 0, Pi}]
xt = x /. FindRoot[x + Tan[x] == 0, {x, 1.5, 2.5}, WorkingPrecision -> 100]
RealDigits[xt]   (* A196504 *)
c = N[xt*Sin[xt], 100]
RealDigits[c]    (* A196765 *)
slope = Cos[xt]
RealDigits[slope](* A196766 *)
(* 2nd program for A196765 by Rick L. Shepherd, Jan 12 2014 *)
RealDigits[N[MaxValue[{x*Sin[x], x>1 && x<3}, {x}], 120]]

Extensions

More terms from Rick L. Shepherd, Jan 12 2014