A188886 Continued fraction of (1+sqrt(1+e^2))/e.

1, 2, 3, 3, 1, 15, 1, 3, 7, 1, 2, 4, 2, 1, 4, 1, 1, 12, 4, 52, 1, 2, 1, 7, 3, 6, 1, 21, 1, 11, 1, 4, 1, 3, 2, 3, 2, 7, 1, 1, 2, 1, 3, 2, 1, 43, 4, 1, 1, 4, 4, 18, 2, 4, 4, 2, 1, 2, 3, 1, 3, 9, 1, 9, 4, 1, 6, 1, 1, 1, 2, 10, 1, 1, 1, 1, 2, 1, 2, 1, 2, 21, 2, 2, 1, 4, 1, 3, 12, 1, 9, 6, 1, 1, 4, 5, 2, 1, 1, 1, 1, 3, 1, 3, 16, 1, 6, 3, 10, 1, 8, 1, 8, 1, 13, 21, 1, 2, 4, 1

Offset

0,2

Comments

For a geometric interpretation, see A188640 and A188885.

Links

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

Example

(1+sqrt(1+e^2))/e=[1,2,3,3,1,15,1,3,7,1,2,4,...].

Mathematica

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

Crossrefs

Cf. A188640, A188885 (decimal expansion).

Sequence in context: A068008 A123948 A329430 * A131012 A083057 A099028

Adjacent sequences: A188883 A188884 A188885 * A188887 A188888 A188889

Keyword

nonn,cofr

Author

Clark Kimberling, Apr 12 2011

Extensions

Offset changed by Andrew Howroyd, Jul 08 2024

Status

approved