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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
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.
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
(PARI) (4+5*sqrt(2))/4 \\ G. C. Greubel, Jan 13 2018
(Magma) (4+5*Sqrt(2))/4 // G. C. Greubel, Jan 13 2018
CROSSREFS
Cf. A188635.
Sequence in context: A103557 A210963 A210965 * A158241 A156591 A233770
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 02 2011
STATUS
approved

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Last modified April 12 17:42 EDT 2024. Contains 371635 sequences. (Running on oeis4.)