login
A263209
Decimal expansion of the imaginary part of the continued fraction i/(e + i/(e + i/(...))).
2
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, 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, 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
OFFSET
0,1
COMMENTS
Here, i is the imaginary unit sqrt(-1) and e is the Euler number.
For the real part of this constant, and for more comments, see A263208.
LINKS
FORMULA
Equals the imaginary part of (sqrt(e^2 + 4 * i) - e)/2.
EXAMPLE
0.355881727107562782631319498137529743468727927576648116645325368688...
MAPLE
evalf((16 + exp(4))^(1/4) * sin(arctan(4/exp(2))/2) / 2, 120); # Vaclav Kotesovec, Nov 06 2015
MATHEMATICA
RealDigits[Im[(Sqrt[E^2 + 4I] - E)/2], 10, 100][[1]] (* Alonso del Arte, Oct 12 2015 *)
PROG
(PARI) imag((-exp(1)+sqrt(exp(2)+4*I))/2)
CROSSREFS
Sequence in context: A019632 A021285 A138575 * A101330 A063285 A316938
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Oct 12 2015
STATUS
approved