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A189961 Decimal expansion of (5+7*sqrt(5))/10. 3
2, 0, 6, 5, 2, 4, 7, 5, 8, 4, 2, 4, 9, 8, 5, 2, 7, 8, 7, 4, 8, 6, 4, 2, 1, 5, 6, 8, 1, 1, 1, 8, 9, 3, 3, 6, 4, 8, 0, 8, 4, 3, 2, 8, 5, 1, 7, 2, 8, 0, 6, 8, 0, 0, 6, 9, 8, 9, 6, 2, 8, 0, 7, 1, 7, 8, 7, 3, 6, 4, 6, 4, 7, 9, 4, 6, 4, 6, 3, 4, 2, 9, 5, 9, 0, 0, 9, 0, 0, 8, 5, 8, 6, 5, 1, 4, 7, 5, 9, 2, 4, 7, 8, 6, 5, 5, 7, 2, 3, 3, 0, 5, 5, 4, 1, 6, 4, 8, 4, 5, 2, 9, 7, 7, 2, 8, 7, 4, 0, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The constant at A189961 is the shape of a rectangle whose continued fraction partition consists of 3 golden rectangles.  For a general discussion, see A188635.

LINKS

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

FORMULA

Continued fraction (as explained at A188635): [r,r,r], where r = (1 + sqrt(5))/2. Ordinary continued fraction, as given by Mathematica program shown below:

[2,15,3,15,3,15,3,15,3,...]

MATHEMATICA

r=(1+5^(1/2))/2;

FromContinuedFraction[{r, r, r}]

FullSimplify[%]

N[%, 130]

RealDigits[%]  (* A189961 *)

ContinuedFraction[%%]

PROG

(PARI) (5+7*sqrt(5))/10 \\ G. C. Greubel, Jan 13 2018

(MAGMA) (5+7*Sqrt(5))/10 // G. C. Greubel, Jan 13 2018

CROSSREFS

Cf. A188635, A189962, A189963.

Sequence in context: A142457 A100711 A199464 * A211241 A140247 A271170

Adjacent sequences:  A189958 A189959 A189960 * A189962 A189963 A189964

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, May 02 2011

STATUS

approved

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Last modified October 18 04:57 EDT 2019. Contains 328145 sequences. (Running on oeis4.)