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

Author

Clark Kimberling, Apr 10 2011

Keywords

• nonn
• cofr

Comments

See A188640 for the origin of this constant.

Crossrefs

Cf. A188640 (decimal expansion), A188721.

Programs

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]

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,...].

Extensions

Offset changed by Andrew Howroyd, Jul 07 2024