A263209 - OEIS

%I #13 Nov 08 2015 02:44:42

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

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

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

%N Decimal expansion of the imaginary part of the continued fraction i/(e + i/(e + i/(...))).

%C Here, i is the imaginary unit sqrt(-1) and e is the Euler number.

%C For the real part of this constant, and for more comments, see A263208.

%H Stanislav Sykora, <a href="/A263209/b263209.txt">Table of n, a(n) for n = 0..2000</a>

%F Equals the imaginary part of (sqrt(e^2 + 4 * i) - e)/2.

%e 0.355881727107562782631319498137529743468727927576648116645325368688...

%p evalf((16 + exp(4))^(1/4) * sin(arctan(4/exp(2))/2) / 2, 120); # _Vaclav Kotesovec_, Nov 06 2015

%t RealDigits[Im[(Sqrt[E^2 + 4I] - E)/2], 10, 100][[1]] (* _Alonso del Arte_, Oct 12 2015 *)

%o (PARI) imag((-exp(1)+sqrt(exp(2)+4*I))/2)

%Y Cf. A001113, A263208.

%K nonn,cons

%O 0,1

%A _Stanislav Sykora_, Oct 12 2015