A188931 Continued fraction of sqrt(5)+sqrt(6).

4, 1, 2, 5, 1, 1, 4, 1, 2, 24, 1, 2, 4, 2, 1, 3, 8, 3, 1, 2, 1, 1, 1, 40, 3, 1, 3, 1, 3, 3, 5, 14, 1, 5, 3, 6, 1, 9, 3, 1, 1, 10, 1, 2, 2, 1, 1, 23, 6, 4, 1, 1, 4, 1, 3, 21, 1, 3, 4, 1, 2, 1, 1, 1, 1, 4, 54, 8, 2, 3, 1, 6, 1, 6, 3, 2, 32, 1, 1, 4, 2, 1, 1, 2, 1, 1, 6, 1, 4, 2, 2, 1, 1, 1, 3, 14, 1, 11, 2, 3, 6, 32, 1, 1, 1, 8, 1, 1, 1, 3, 1, 2, 1, 10, 1, 4, 4, 1, 2, 1

Offset: 0

Author

Clark Kimberling, Apr 13 2011

Keywords

• nonn
• cofr

Comments

For a geometric interpretation, see A188640 and A188930.

Examples

			sqrt(5)+sqrt(6)=[4,1,2,5,1,1,4,1,2,24,...].
		

Crossrefs

Cf. A188930 (decimal expansion).

Programs

Mathematica

r = 20^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
ContinuedFraction[Sqrt[5]+Sqrt[6],120] (* Harvey P. Dale, Jun 26 2021 *)

Extensions

Offset changed by Andrew Howroyd, Jul 08 2024