A188627 Continued fraction of e+sqrt(e^2-1).

5, 4, 15, 6, 1, 13, 2, 1, 1, 21, 3, 2, 16, 1, 4, 1, 1, 157, 1, 9, 1, 3, 1, 5, 1, 2, 1, 3, 1, 1, 1, 1, 11, 1, 1, 22, 1, 9, 1, 1, 1, 1, 12, 1, 7, 6, 1, 3, 2, 8, 1, 1, 1, 1, 4, 2, 3, 1, 10, 17, 1, 2, 1, 5, 8, 1, 2, 1, 6, 1, 12, 1, 39, 16, 14, 1, 46, 72, 16, 3, 1, 1, 5, 2, 1, 5, 2, 1, 10, 4, 2, 2, 3, 2, 1, 3, 2, 2, 27, 10, 4, 2, 8, 1, 2, 6, 3, 945, 1, 1, 106, 1, 1, 3, 1, 2, 6, 1, 1, 2

Offset: 0

Author

Clark Kimberling, Apr 11 2011

Keywords

• nonn
• cofr

Examples

			e+sqrt(e^2-1) = [5, 4, 15, 6, 1, 13, 2, 1, 1, 21, 3, 2, 16, 1, ...]
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A188739 (decimal expansion).

Programs

Magma

SetDefaultRealField(RealField(100)); ContinuedFraction(Exp(1) + Sqrt(Exp(2) - 1)); // G. C. Greubel, Nov 01 2018

Mathematica

r = 2 E; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]] (* A188739 *)
ContinuedFraction[t, 120] (* A188627 *)

PARI

default(realprecision, 100); contfrac(exp(1) + sqrt(exp(2) - 1)) \\ G. C. Greubel, Nov 01 2018

Extensions

Offset changed by Andrew Howroyd, Aug 08 2024