A188728 Continued fraction of (e+sqrt(16+e^2))/4.

1, 1, 7, 1, 46, 8, 30, 1, 5, 4, 2, 6, 3, 2, 5, 1, 1, 1, 3, 50, 1, 3, 1, 1, 3, 1, 45, 1, 1, 1, 4, 1, 1, 2, 8, 2, 35, 2, 1, 27, 6, 112, 1, 113, 16, 1, 11, 1, 1, 6, 1, 12, 1, 3, 2, 15, 1, 2, 1, 1, 5, 1, 16, 2, 2, 2, 1, 10, 1, 43, 1, 13, 1, 6, 1, 4, 1, 2, 1, 1, 1, 6, 1, 8, 8, 1, 6, 3, 3, 17, 3, 1, 27, 1, 11, 1, 1, 1, 1, 1, 1, 9, 7, 2, 1, 5, 5, 7, 6, 2, 1, 5, 1, 2, 1, 5, 57, 8, 2, 1

Offset: 0

Author

Clark Kimberling, Apr 10 2011

Keywords

• nonn
• cofr

Comments

See A188727 for the origin of the constant.

Examples

			(e+sqrt(16+e^2))/4 = [1,1,7,1,46,30,1,5,4,...].
		

Links

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

Crossrefs

Cf. A188640, A188727 (decimal expansion).

Programs

Magma

SetDefaultRealField(RealField(100)); ContinuedFraction((Exp(1)  + Sqrt(16 + Exp(2)))/4); // G. C. Greubel, Oct 31 2018

Mathematica

r = e/2; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]] (* A188727 *)
ContinuedFraction[t, 120] (* A188728 *)

PARI

default(realprecision, 100); contfrac((exp(1) + sqrt(16 + exp(2)))/4) \\ G. C. Greubel, Oct 31 2018

Extensions

Offset changed by Andrew Howroyd, Aug 08 2024