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%I #8 Aug 03 2021 12:51:37
%S 2,9,3,8,1,0,0,3,9,3,9,7,0,8,1,1,8,0,7,6,5,8,1,3,6,4,7,8,4,2,5,9,1,2,
%T 9,5,9,6,7,0,2,1,8,6,1,7,3,2,2,3,1,0,1,7,8,4,6,7,1,7,6,3,8,5,3,5,4,6,
%U 7,8,5,9,2,9,2,8,3,6,7,4,6,4,2,0,8,7,7,5,5,2,1,0,3,9,6,7,7,7,3,9
%N Decimal expansion of greatest x satisfying x+3*cos(x) = 0.
%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%e least: -1.1701209500026260537060430118589710...
%e greatest: 2.9381003939708118076581364784259...
%t a = 1; b = 3; c = 0;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -1.5, 3.5}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199603 least of 4 roots *)
%t r = x /. FindRoot[f[x] == g[x], {x, 2.93, 2.94}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199604 greatest of 4 roots *)
%Y Cf. A199597.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Nov 08 2011
%E a(86) onwards corrected by _Georg Fischer_, Aug 03 2021
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