%I #5 Mar 30 2012 18:57:50

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

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

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

%N Decimal expansion of the least x>0 satisfying 1/(1+x^2)=4*sin(x).

%e x=0.238777659445904852564729030954613747638153989...

%t Plot[{1/(1 + x^2), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, 2}]

%t t = x /. FindRoot[1 == (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196825 *)

%t t = x /. FindRoot[1 == 2 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196826 *)

%t t = x /. FindRoot[1 == 3 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196827 *)

%t t = x /. FindRoot[1 == 4 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196828 *)

%t t = x /. FindRoot[1 == 5 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196829 *)

%t t = x /. FindRoot[1 == 6 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196830 *)

%Y Cf. A196832.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 07 2011