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

%I #7 Feb 07 2025 16:44:05

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

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

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

%N Decimal expansion of x>0 satisfying 4*x^2-3x=3*sin(x).

%C See A198414 for a guide to related sequences. The Mathematica program includes a graph.

%e x=1.304631710394787379587467065232993969376072...

%t a = 4; b = -3; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -.2, 1.5}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.30, 1.31}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198575 *)

%Y Cf. A198414.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 27 2011