|
|
A189959
|
|
Decimal expansion of (4+5*sqrt(2))/4.
|
|
3
|
|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
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.
|
|
LINKS
|
|
|
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...]
|
|
EXAMPLE
|
2.767766952966368811002110905262122598212089844221...
|
|
MATHEMATICA
|
r=1+2^(1/2);
FromContinuedFraction[{r, r, r}]
FullSimplify[%]
N[%, 130]
RealDigits[%]
ContinuedFraction[%%]
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|