|
%I #5 Mar 30 2012 18:57:56
%S 3,0,6,7,5,5,3,5,4,1,3,7,7,5,3,0,0,7,0,1,1,6,5,1,6,3,4,7,3,3,3,6,0,1,
%T 4,7,8,3,9,0,9,6,1,9,0,2,7,0,1,9,8,4,5,7,0,9,0,6,8,2,0,2,0,1,6,0,2,4,
%U 1,5,1,1,8,4,1,3,1,8,1,3,2,9,5,8,2,5,5,6,2,4,2,4,6,7,4,5,1,5,2
%N Decimal expansion of x>0 satisfying x^2+3*sin(x)=1.
%C See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%e negative: -1.946877744670682908335473546697723...
%e positive: 0.30675535413775300701165163473336014...
%t a = 1; b = 3; c = 1;
%t f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -2, -1.9}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199054 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .3, .31}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199055 *)
%Y Cf. A198866.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 02 2011
|
