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Decimal expansion of x>0 satisfying x^2-4*cos(x)=-1.
2

%I #8 Feb 07 2025 16:44:05

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

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

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

%N Decimal expansion of x>0 satisfying x^2-4*cos(x)=-1.

%C See A198755 for a guide to related sequences. The Mathematica program includes a graph.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e 1.0297040007360545584116792679829069589455888...

%t a = 1; b = -4; c = -1;

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

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.02, 1.03}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198842 *)

%Y Cf. A198755.

%K nonn,cons,changed

%O 1,3

%A _Clark Kimberling_, Oct 30 2011