A189959 Decimal expansion of (4+5*sqrt(2))/4.

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

Offset: 1

Author

Clark Kimberling, May 02 2011

Keywords

• nonn
• cons

Comments

Essentially the same as A020789. - R. J. Mathar, May 16 2011

The constant at A189959 is the shape of a rectangle whose continued fraction partition consists of 3 silver rectangles. For a general discussion, see A188635.

Examples

			2.767766952966368811002110905262122598212089844221...
		

Links

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

Crossrefs

Cf. A188635.

Programs

Magma

(4+5*Sqrt(2))/4 // G. C. Greubel, Jan 13 2018

Mathematica

r=1+2^(1/2);
FromContinuedFraction[{r,r,r}]
FullSimplify[%]
N[%,130]
RealDigits[%]
ContinuedFraction[%%]
RealDigits[(4+5Sqrt[2])/4,10,150][[1]] (* Harvey P. Dale, Dec 17 2024 *)

PARI

(4+5*sqrt(2))/4 \\ G. C. Greubel, Jan 13 2018

Formula

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

[2,1,3,3,3,1,2,1,3,3,3,1,2,1,3,3,3,1,2,1,3,3,3,1,2...]