A196826 - OEIS

%I #7 Aug 09 2021 14:08:57

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

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

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

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

%e x=0.43420254999819638681352442196668401983962380...

%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