A188927 Continued fraction of sqrt((7+sqrt(13))/6).

1, 3, 28, 1, 2, 2, 42, 1, 1, 1, 4, 2, 2, 5, 3, 1, 6, 12, 1, 9, 1, 2, 14, 2, 1, 3, 1, 16, 3, 2, 1, 1, 1, 1, 2, 34, 1, 3, 5, 1, 2, 2, 1, 27, 1, 1, 4, 3, 1, 3, 1, 16, 1, 7, 2, 15, 1, 30, 1, 78, 1, 2, 1, 6, 5, 1, 1, 5, 1, 393, 3, 13, 2, 1, 2, 1, 5, 1, 7, 1, 31, 2, 1, 3, 1, 24, 1, 1, 5, 1, 2, 1, 2, 1, 4, 6, 10, 1, 10, 8, 1, 12, 73, 1, 2, 2, 1, 17, 1, 1, 1, 24, 1, 1, 3, 14, 1, 1, 1, 4

Offset: 0

Author

Clark Kimberling, Apr 13 2011

Keywords

• nonn
• cofr

Comments

For a geometric interpretation, see A188640 and A188926.

Examples

			sqrt((7+sqrt(13))/6)=[1,3,28,1,2,2,42,1,1,1,4,2,2,5,...].
		

Crossrefs

Cf. A188640, A188926 (decimal expansion).

Programs

Mathematica

r = 3^(-1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]

Extensions

Offset changed by Andrew Howroyd, Jul 08 2024