A189963 Decimal expansion of (5+9*sqrt(5))/12.

2, 0, 9, 3, 7, 1, 7, 6, 4, 9, 7, 9, 1, 5, 0, 8, 9, 3, 8, 9, 7, 3, 5, 4, 6, 9, 1, 8, 2, 1, 5, 1, 2, 3, 8, 4, 3, 2, 4, 7, 1, 3, 0, 4, 3, 6, 3, 7, 5, 3, 1, 0, 9, 5, 9, 8, 6, 9, 8, 3, 9, 6, 0, 0, 7, 2, 4, 5, 5, 7, 3, 6, 0, 8, 9, 5, 0, 2, 0, 3, 4, 1, 2, 2, 7, 4, 7, 7, 4, 7, 2, 9, 5, 0, 7, 5, 3, 3, 7, 2, 8, 9, 3, 7, 9, 7, 7, 9, 8, 7, 7, 9, 7, 4, 7, 0, 0, 4, 2, 9, 4, 8, 5, 6, 6, 1, 7, 4, 6, 0

Offset

1,1

Comments

The constant at A189963 is the shape of a rectangle whose continued fraction partition consists of 5 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 A189959): [r,r,r,r,r], where r=(1+sqrt(5))/2. Ordinary continued fraction, as given by Mathematica program shown below:

[2,10,1,2,29,1,5,2,1,1,2,1,3,5,1,3,3,10,1,2,29,...].

Example

2.09371764979150893897354691821512384324713043637531095986983...

Mathematica

r=(1+5^(1/2))/2;
FromContinuedFraction[{r, r, r, r, r}]
FullSimplify[%]
N[%, 130]
RealDigits[%]  (*A189963*)
ContinuedFraction[%%]

Prog

(PARI) (5+9*sqrt(5))/12 \\ G. C. Greubel, Jan 13 2018
(Magma) (5+9*Sqrt(5))/12 // G. C. Greubel, Jan 13 2018

Crossrefs

Cf. A188635, A189961, A189962.

Sequence in context: A198735 A071120 A249417 * A156649 A197330 A343882

Adjacent sequences: A189960 A189961 A189962 * A189964 A189965 A189966

Keyword

nonn,cons

Author

Clark Kimberling, May 02 2011

Status

approved