

A189960


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


1



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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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.


LINKS



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,...]


EXAMPLE

2.7755156578866803716262115031565793012577141550...


MATHEMATICA

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


PROG



CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



