A190263 Continued fraction of (3 + sqrt(9 + 12*sqrt(3)))/6.

1, 2, 2, 3, 1, 3, 2, 1, 1, 1, 1, 8, 2, 17, 2, 3, 10, 2, 23, 1, 4, 1, 2, 1, 4, 1, 2, 35, 4, 1, 1, 1, 2, 5, 4, 1, 1, 3, 17, 3, 2, 1, 3, 1, 3, 1, 1, 10, 3, 1, 13, 1, 1, 1, 4, 1, 2, 2, 2, 1, 2, 15, 3, 2, 5, 6, 2, 1, 15, 132, 4, 2, 1, 1, 19, 1, 4, 1, 2, 5, 2, 16, 2, 1, 15, 5, 2, 10, 13, 1, 1

Offset: 1

Author

Clark Kimberling, May 06 2011

Keywords

• nonn
• cofr

Comments

Equivalent to the periodic continued fraction [1, x, 1, x,...], where x=sqrt(3). (See A188635.)

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A188635, A190262.

Programs

Magma

ContinuedFraction((3 + sqrt(9 + 12*sqrt(3)))/6); // G. C. Greubel, Dec 28 2017

Mathematica

r=3^(1/2)
FromContinuedFraction[{1, r, {1, r}}]
FullSimplify[%]
ContinuedFraction[%, 100]  (* A190263 *)
RealDigits[N[%%, 120]]     (* A190262 *)
N[%%%, 40]
ContinuedFraction[(3 + Sqrt[9 + 12*Sqrt[3]])/6, 100] (* G. C. Greubel, Dec 26 2017 *)

PARI

contfrac((3+sqrt(9+sqrt(432)))/6) \\ Charles R Greathouse IV, Jul 29 2011