A189041 Continued fraction for (e+sqrt(-4+e^2))/2.

2, 3, 1, 1, 2, 1, 3, 2, 1, 1, 2, 2, 1, 3, 3, 2, 1, 1, 1, 2, 23, 1, 1, 2, 33, 1, 1, 3, 1, 1, 20, 5, 40, 1, 3, 1, 25, 1, 2, 1, 26, 1, 6, 3, 1, 5, 5, 7, 1, 24, 5, 14, 1, 1, 2, 1, 8, 2, 1, 1, 10, 1, 1, 2, 1, 2, 2, 1440, 2, 17, 1, 1, 3, 4, 1, 18, 2, 1, 1, 1, 8, 1, 5, 1, 4, 18, 1, 3, 5, 1, 24, 3, 4, 1, 1, 4, 4, 1, 137, 3, 1, 1, 1, 6, 1, 1, 7, 1, 1, 2, 6, 1, 1, 5, 1, 2, 5, 7, 1, 3

Offset

0,1

Links

Table of n, a(n) for n=0..119.

Example

(e+sqrt(-4+e^2))/2=[2,3,1,1,2,1,3,2,1,1,2,2,...]

Mathematica

r = E; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]

Crossrefs

Cf. A189040 (decimal expansion).

Sequence in context: A191770 A120966 A373354 * A055444 A102383 A070913

Adjacent sequences: A189038 A189039 A189040 * A189042 A189043 A189044

Keyword

nonn,cofr

Author

Clark Kimberling, Apr 15 2011

Extensions

Offset changed by Andrew Howroyd, Jul 08 2024

Status

approved