A189960 Decimal expansion of (9+27*sqrt(2))/17.

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

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

Index entries for algebraic numbers, degree 2.

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,...]

Minimal polynomial: 17*x^2 - 18*x - 81. - Amiram Eldar, Jun 06 2026

Example

2.7755156578866803716262115031565793012577141550...

Mathematica

r = 1 + 2^(1/2);
FromContinuedFraction[{r, r, r, r}]
FullSimplify[%]
N[%, 150]
RealDigits[%]
(* Alternative: *)
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 A377996

Adjacent sequences: A189957 A189958 A189959 * A189961 A189962 A189963

Keyword

nonn,cons,changed

Author

Clark Kimberling, May 02 2011

Status

approved