A199159 - OEIS

%I #5 Mar 30 2012 18:57:57

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

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

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

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

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

%e negative: -1.1082694473937105467280082158614997423379...

%e positive:  0.2658016271983479815831296920342773310942...

%t a = 3; b = 3; 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 /.

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

%t RealDigits[r]   (* A199158 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .26, .27}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A199159 *)

%Y Cf. A198866.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 03 2011