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A196619 Decimal expansion of the number c for which the curve y=cos(x) is tangent to the curve y=(1/x)-c, and 0

%I A196619 #9 Aug 22 2018 05:06:51
%S A196619 4,5,4,4,5,1,8,6,6,3,5,4,2,2,6,5,9,9,8,1,9,6,9,1,1,4,6,3,2,9,5,2,3,4,
%T A196619 0,2,8,3,6,3,4,6,9,6,1,1,7,9,5,6,7,2,2,1,8,1,1,7,2,6,3,4,1,4,5,1,2,5,
%U A196619 7,1,7,1,7,6,6,8,0,0,5,9,9,3,4,9,4,8,5,0,9,9,7,9,0,1,6,0,2,7,2
%N A196619 Decimal expansion of the number c for which the curve y=cos(x) is tangent to the curve y=(1/x)-c, and 0<x<2*Pi.
%H A196619 G. C. Greubel, <a href="/A196619/b196619.txt">Table of n, a(n) for n = 0..10000</a>
%e A196619 x = 0.454451866354226599819691146329523402836346961...
%t A196619 Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
%t A196619 xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
%t A196619 RealDigits[xt]      (* A196617 *)
%t A196619 Cos[xt]
%t A196619 RealDigits[Cos[xt]] (* A196618 *)
%t A196619 c = N[1/xt - Cos[xt], 100]
%t A196619 RealDigits[c]       (* A196619 *)
%t A196619 slope = -Sin[xt]
%t A196619 RealDigits[slope]   (* A196620 *)
%o A196619 (PARI) a=1; c=0; x=solve(x=1, 1.5, a*x^2 + c - 1/sin(x)); 1/x - cos(x) \\ _G. C. Greubel_, Aug 22 2018
%Y A196619 Cf. A196617, A196618, A196620, A196612.
%K A196619 nonn,cons
%O A196619 0,1
%A A196619 _Clark Kimberling_, Oct 05 2011