A188888 Continued fraction of sqrt(2 + sqrt(3)) or 2*cos(Pi/12).

1, 1, 13, 1, 2, 15, 10, 1, 18, 1, 1, 21, 2, 1, 1, 2, 4, 5, 2, 2, 2, 11, 1, 2, 2, 3, 1, 1, 10, 1, 2, 1, 2, 3, 2, 3, 15, 1, 2, 3, 1, 1, 90, 1, 44, 2, 4, 10, 1, 11, 9, 1, 17, 1, 8, 2, 2, 6, 2, 6, 1, 3, 1, 1, 1, 2, 20, 1, 7, 27, 1, 19, 40, 1, 304, 1, 1, 2, 1, 1, 1, 62, 1, 1, 2, 1, 2, 1, 32, 1, 1, 1, 11, 1, 20, 1, 85, 1, 1, 1, 3, 3, 13, 1, 4, 1, 3, 1, 3, 1, 16, 1, 9, 3, 2, 1, 1, 30, 2, 1

Offset: 0

Author

Clark Kimberling, Apr 12 2011

Keywords

• nonn
• cofr

Comments

For a geometric interpretation, see A188640 and A188887.

Examples

			sqrt(2+sqrt(3)) = [1,1,13,1,2,15,10,1,18,1,1,21,2,1,1,2,4,...].
		

Links

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

Crossrefs

Cf. A188887 (decimal expansion).

Programs

Magma

SetDefaultRealField(RealField(100));  ContinuedFraction(Sqrt(2 + Sqrt(3))); // G. C. Greubel, Sep 29 2018

Maple

with(numtheory): cfrac(sqrt(2+sqrt(3)),120,'quotients'); # Muniru A Asiru, Sep 30 2018

Mathematica

r = 2^(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[2+Sqrt[3]],120] (* Harvey P. Dale, Jul 19 2014 *)

PARI

default(realprecision, 100); contfrac(sqrt(2 + sqrt(3))) \\ G. C. Greubel, Sep 29 2018

Extensions

Name extended by Greg Dresden, Apr 13 2018

Offset changed by Andrew Howroyd, Aug 08 2024