A188796 Continued fraction of e+sqrt(1+e^2).

5, 1, 1, 1, 1, 2, 7, 1, 7, 3, 1, 5, 2, 5, 1, 1, 1, 3, 6, 8, 26, 2, 1, 2, 3, 1, 1, 1, 13, 1, 10, 2, 5, 1, 10, 1, 1, 4, 1, 1, 2, 1, 3, 3, 2, 7, 1, 2, 21, 1, 1, 1, 1, 3, 2, 8, 9, 4, 2, 8, 1, 2, 1, 7, 1, 1, 19, 1, 4, 9, 1, 2, 1, 4, 2, 1, 4, 1, 4, 6, 2, 5, 10, 1, 2, 2, 10, 1, 1, 25, 1, 4, 13, 9, 2, 1, 2, 4, 8, 1, 1, 33, 1, 2, 1, 1, 1, 21, 1, 3, 1, 18, 1, 6, 43, 2, 1, 1, 1, 8

Offset

0,1

Comments

See A188640 for the origin of this constant.

Links

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

Formula

e+sqrt(1+e^2)) = 5.614668.. = [5,1,1,1,1,2,7,1,7,3,1,5,2,5,1,1,1,...].

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 (decimal expansion), A188721.

Sequence in context: A369874 A340366 A031261 * A161685 A257461 A129398

Adjacent sequences: A188793 A188794 A188795 * A188797 A188798 A188799

Keyword

nonn,cofr

Author

Clark Kimberling, Apr 10 2011

Extensions

Offset changed by Andrew Howroyd, Jul 07 2024

Status

approved