A138284 - OEIS

%I #2 Mar 30 2012 17:22:47

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

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

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

%N Decimal expansion of the negative real part of z0, the smallest second-quadrant solution of z = Cos(z).

%C z0 is a repelling fixed point of Cos(z). The only fixed point on the real axis is 0.73908... (A003957), which is an attracting fixed point.

%e 2.486885698908560230696957...

%t z0 = FindRoot[{Re[Cos[x+I*y]]==x, Im[Cos[x+I*y]]==y}, {{x,-2},{y,2}}, WorkingPrecision->150]; RealDigits[z0[[1,2]]]

%Y Cf. A138285 (imaginary part).

%K cons,nonn

%O 1,1

%A _T. D. Noe_, Mar 12 2008