OFFSET
0,1
COMMENTS
The real part, 1.300242590..., is given by A156548.
Coincides with the limit of the imaginary part of the same expression, but with f(z)=i/(1+z), and therefore with the imaginary part of the continued fraction i/(1+i/(1+i/(...))). It is also equal to the real part of the continued fraction i/(i+i/(i+i/(...))). - Stanislav Sykora, May 27 2015
FORMULA
Define z(1)=f(0)=sqrt(i), where i=sqrt(-1), and z(n)=f(z(n-1)) for n>1.
Write the limit of z(n) as a+bi where a and b are real. Then a=(b+1)/(2b), where b=sqrt((sqrt(17)-1)/8).
EXAMPLE
0.6248105338...
MATHEMATICA
RealDigits[Sqrt[(Sqrt[17]-1)/8], 10, 120][[1]] (* Vaclav Kotesovec, May 28 2015 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Feb 12 2009
STATUS
approved