A189960 Decimal expansion of (9+27*sqrt(2))/17.

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

Offset: 1

Author

Clark Kimberling, May 02 2011

Keywords

• nonn
• cons

Comments

The constant at A189960 is the shape of a rectangle whose continued fraction partition consists of 4 silver rectangles. For a general discussion, see A188635.

Examples

			2.7755156578866803716262115031565793012577141550...
		

Links

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

Crossrefs

Cf. A188635, A189959.

Programs

Magma

(9+27*Sqrt(2))/17 // G. C. Greubel, Jan 13 2018

Mathematica

r = 1 + 2^(1/2);
FromContinuedFraction[{r,r,r,r}]
FullSimplify[%]
N[%, 150]
RealDigits[%]  (*A189960*)
ContinuedFraction[%%, 120]
RealDigits[(9+27Sqrt[2])/17,10,150][[1]] (* Harvey P. Dale, Dec 22 2019 *)

PARI

(9+27*sqrt(2))/17 \\ G. C. Greubel, Jan 13 2018

Formula

Continued fraction (as explained at A188635): [r,r,r,r], where r = 1 + sqrt(2). The ordinary continued fraction (as given by Mathematica program shown below) is as follows: [2,1,3,2,5,76,5,2,3,1,3,1,2,1,1,7,1,10,38,10,...]