cp's OEIS Frontend

A156590 Decimal expansion of the imaginary part of the limit of f(f(...f(0)...)) where f(z)=sqrt(i+z).

%I A156590 #14 Jun 18 2015 05:56:48
%S A156590 6,2,4,8,1,0,5,3,3,8,4,3,8,2,6,5,8,6,8,7,9,6,0,4,4,4,7,4,4,2,8,5,1,4,
%T A156590 4,4,0,0,5,2,3,4,4,5,6,4,1,9,0,0,2,3,2,7,4,7,0,1,5,4,3,1,4,6,5,3,1,7,
%U A156590 1,0,5,5,4,3,9,4,9,6,4,0,7,0,5,2,4,5,2,8,9,1,2,7,5,5,3,2,9,5,0,9,1,7,3,1,7
%N A156590 Decimal expansion of the imaginary part of the limit of f(f(...f(0)...)) where f(z)=sqrt(i+z).
%C A156590 The real part, 1.300242590..., is given by A156548.
%C A156590 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
%F A156590 Define z(1)=f(0)=sqrt(i), where i=sqrt(-1), and z(n)=f(z(n-1)) for n>1.
%F A156590 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).
%e A156590 0.6248105338...
%t A156590 RealDigits[Sqrt[(Sqrt[17]-1)/8],10,120][[1]] (* _Vaclav Kotesovec_, May 28 2015 *)
%Y A156590 Cf. A156548.
%K A156590 nonn,cons
%O A156590 0,1
%A A156590 _Clark Kimberling_, Feb 12 2009