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%I #8 Jun 24 2018 16:03:08
%S 1,6,6,9,6,9,2,1,6,9,6,4,9,7,6,3,4,5,8,2,5,2,8,3,8,3,0,5,9,8,4,9,1,7,
%T 3,3,5,9,3,7,7,5,8,9,9,6,5,9,1,6,9,9,1,6,8,2,8,2,4,0,8,4,9,6,1,1,2,9,
%U 1,0,5,6,2,3,4,4,1,3,3,4,1,9,3,2,5,7,8,3,8,7,2,9,5,5,6,9,3,4,7
%N Decimal expansion of greatest x satisfying x^2 - 2*cos(x) = 3*sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200023/b200023.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.514514830476458686565638945675371815952...
%e greatest x: 1.66969216964976345825283830598491733593...
%t a = 1; b = -2; c = 3;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.52, -.51}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200022 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.66, 1.67}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200023 *)
%o (PARI) a=1; b=-2; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 13 2011
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