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Decimal expansion of x>0 having x^2-x=sin(x).
2

%I #6 Feb 07 2025 16:44:05

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

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

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

%N Decimal expansion of x>0 having x^2-x=sin(x).

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

%e x=1.6175452860622547530274288138205252801...

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

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

%t Plot[{f[x], g[x]}, {x, -1, 2}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198420 *)

%Y Cf. A198414.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 24 2011