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Decimal expansion of x > 0 satisfying 2*x^2+2*sin(x) = 1.
3

%I #7 Aug 01 2021 13:45:33

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

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

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

%N Decimal expansion of x > 0 satisfying 2*x^2+2*sin(x) = 1.

%C See A198866 for a guide to related sequences. The Mathematica program includes a graph.

%e negative: -1.19608203329713481914562195294104321159720...

%e positive: 0.37088734011199207060142934573448899294899...

%t a = 2; b = 2; c = 1;

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

%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199067 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .37, .38}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199068 *)

%Y Cf. A198866.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 02 2011

%E a(82) onwards corrected by _Georg Fischer_, Aug 01 2021