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%I #8 Jun 25 2018 22:54:01
%S 1,7,6,9,5,6,8,8,7,4,3,7,2,7,0,1,7,4,9,1,1,5,0,7,8,4,6,2,0,0,1,6,2,7,
%T 7,5,4,7,6,5,5,5,3,4,1,0,5,3,8,0,6,4,0,4,0,5,3,9,9,1,8,7,9,8,4,0,5,9,
%U 5,2,4,5,4,0,9,7,9,4,2,2,5,4,4,0,2,3,5,1,2,0,1,4,4,1,5,7,7,4,0
%N Decimal expansion of greatest x satisfying x^2 - 4*cos(x) = 4*sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200106/b200106.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.698933604732903309337989544733567956233...
%e greatest x: 1.7695688743727017491150784620016277547...
%t a = 1; b = -4; c = 4;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.7, -.6}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200105 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.76, 1.77}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200106 *)
%o (PARI) a=1; b=-4; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 25 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 13 2011
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