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

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

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

%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 1.358092349796935915229344782948732183383...

%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, 1.3, 1.4}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198838 *)

%Y Cf. A198755.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Oct 30 2011