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Decimal expansion of least x having x^2-2x=-cos(x).
3

%I #5 Mar 30 2012 18:57:53

%S 5,8,9,3,0,3,2,0,8,1,5,9,0,1,2,8,7,4,7,2,5,2,2,3,9,1,9,0,7,3,8,6,9,1,

%T 8,5,8,8,9,0,6,0,9,8,8,0,5,4,0,7,0,3,0,5,5,3,9,2,1,4,0,7,5,1,1,7,1,4,

%U 5,7,1,7,7,0,6,4,7,2,4,1,0,8,8,0,5,2,2,1,0,2,0,0,1,6,9,6,5,6,7

%N Decimal expansion of least x having x^2-2x=-cos(x).

%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.

%e least x: 0.589303208159012874725223919073869185889...

%e greatest x: 2.287086177656584485337033312314491737...

%t a = 1; b = -2; c = -1;

%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]

%t Plot[{f[x], g[x]}, {x, -1, 3}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A197815 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.3}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A197820 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 20 2011