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A198939 Decimal expansion of x>0 satisfying 3*x^2-4*cos(x)=1.

%I A198939 #8 Feb 07 2025 17:57:52
%S A198939 1,0,1,7,0,8,5,5,0,3,3,7,4,3,8,3,1,3,0,7,2,2,0,7,2,0,1,6,7,7,1,6,2,6,
%T A198939 0,8,9,5,6,6,4,6,1,3,4,2,9,6,5,5,5,0,5,7,5,6,2,2,6,6,3,8,0,6,9,1,6,6,
%U A198939 6,5,9,1,8,6,4,6,7,0,0,4,5,6,7,6,5,0,5,7,9,3,4,2,2,8,1,5,8,6,8
%N A198939 Decimal expansion of x>0 satisfying 3*x^2-4*cos(x)=1.
%C A198939 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A198939 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A198939 1.017085503374383130722072016771626089566461...
%t A198939 a = 3; b = -4; c = 1;
%t A198939 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A198939 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A198939 r = x /. FindRoot[f[x] == g[x], {x, 1.01, 1.02}, WorkingPrecision -> 110]
%t A198939 RealDigits[r] (* A198939 *)
%Y A198939 Cf. A198755.
%K A198939 nonn,cons
%O A198939 1,4
%A A198939 _Clark Kimberling_, Nov 01 2011