OFFSET
1,2
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
EXAMPLE
x=1.8197057411596530462069576803755281456165224784...
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]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 06 2011
EXTENSIONS
More terms from Rick L. Shepherd, Jan 12 2014
STATUS
approved