%I #11 Jul 06 2018 03:02:48
%S 4,1,3,7,5,1,7,5,9,1,4,4,7,7,3,9,3,7,6,8,4,4,0,0,2,7,9,8,9,8,9,2,7,5,
%T 6,4,5,9,9,2,2,5,1,3,8,5,5,5,7,8,6,6,1,8,6,3,7,5,1,5,2,8,7,7,7,8,7,6,
%U 3,1,5,3,2,0,3,3,8,4,9,9,6,1,7,4,1,5,9,0,0,6,9,1,1,8,7,6,2,3,7
%N Decimal expansion of least x satisfying 3*x^2 - cos(x) = sin(x), negated.
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200132/b200132.txt">Table of n, a(n) for n = 0..10000</a>
%e least x: -0.4137517591447739376844002798989...
%e greatest x: 0.68485307862320115956369446864...
%t a = 3; b = -1; c = 1;
%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, -.42, -.41}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200132 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .68, .69}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200133 *)
%o (PARI) a=3; b=-1; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y Cf. A199949.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 14 2011
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