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A190263 Continued fraction of (3 + sqrt(9 + 12*sqrt(3)))/6. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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 *)

PROG

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

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

CROSSREFS

Cf. A188635, A190262.

Sequence in context: A265576 A083040 A083899 * A144911 A233431 A160650

Adjacent sequences:  A190260 A190261 A190262 * A190264 A190265 A190266

KEYWORD

nonn,cofr

AUTHOR

Clark Kimberling, May 06 2011

STATUS

approved

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Last modified April 6 20:30 EDT 2020. Contains 333286 sequences. (Running on oeis4.)