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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

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

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]

RealDigits[%]  (*A189960*)

ContinuedFraction[%%, 120]

RealDigits[(9+27Sqrt[2])/17, 10, 150][[1]] (* Harvey P. Dale, Dec 22 2019 *)

PROG

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

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

CROSSREFS

Cf. A188635, A189959.

Sequence in context: A021977 A057105 A016536 * A230160 A063503 A244976

Adjacent sequences:  A189957 A189958 A189959 * A189961 A189962 A189963

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, May 02 2011

STATUS

approved

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Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)