cp's OEIS Frontend

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.

%I A196765 #12 Jan 16 2014 15:09:26
%S A196765 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,
%T A196765 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,
%U A196765 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
%N 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.
%C A196765 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
%e A196765 x=1.8197057411596530462069576803755281456165224784...
%t A196765 Plot[{Sin[x], 1/x, 1.82/x}, {x, 0, Pi}]
%t A196765 xt = x /. FindRoot[x + Tan[x] == 0, {x, 1.5, 2.5}, WorkingPrecision -> 100]
%t A196765 RealDigits[xt]   (* A196504 *)
%t A196765 c = N[xt*Sin[xt], 100]
%t A196765 RealDigits[c]    (* A196765 *)
%t A196765 slope = Cos[xt]
%t A196765 RealDigits[slope](* A196766 *)
%t A196765 (* 2nd program for A196765 by _Rick L. Shepherd_, Jan 12 2014 *)
%t A196765 RealDigits[N[MaxValue[{x*Sin[x], x>1 && x<3}, {x}], 120]]
%Y A196765 Cf. A196760.
%K A196765 nonn,cons
%O A196765 1,2
%A A196765 _Clark Kimberling_, Oct 06 2011
%E A196765 More terms from _Rick L. Shepherd_, Jan 12 2014