A196822 - OEIS

%I #12 Aug 10 2021 21:41:59

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

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

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

%N Decimal expansion of the number x satisfying 2*x = ((1+x^2)^2)*sin(x) and 0 < x < 2*Pi.

%e x=0.686928072507114151477426614944457695958221498999...

%t Plot[{1/(1 + x^2), -.097 + Cos[x]}, {x, 0, 1}]

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

%t RealDigits[t]     (* A196822 *)

%t c = N[-Cos[t] + 1/(1 + t^2), 100]

%t RealDigits[c]     (* A196823 *)

%t slope = N[-Sin[t], 100]

%t RealDigits[slope] (* A196824 *)

%Y Cf. A196823.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 06 2011

%E Definition and a(84) onwards corrected by _Georg Fischer_, Aug 10 2021