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A189968 Decimal expansion of (5+sqrt(85))/6, which has periodic continued fractions [2,2,1,2,2,1,...] and [5/2, 1, 5/2, 1, ...]. 2
2, 3, 6, 9, 9, 2, 4, 0, 7, 6, 2, 1, 5, 4, 8, 1, 2, 1, 8, 3, 3, 3, 7, 1, 2, 3, 8, 0, 2, 9, 3, 7, 9, 8, 8, 5, 9, 5, 4, 1, 1, 3, 4, 1, 7, 4, 7, 8, 7, 0, 7, 7, 3, 3, 4, 6, 6, 7, 9, 5, 8, 7, 0, 0, 9, 0, 7, 1, 1, 1, 8, 3, 7, 8, 0, 0, 3, 1, 2, 5, 7, 6, 7, 9, 4, 6, 4, 9, 0, 1, 5, 1, 3, 2, 2, 1, 3, 4, 2, 7, 4, 9, 0, 0, 5, 6, 6, 3, 4, 8, 1, 3, 1, 4, 5, 2, 8, 0, 6, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let R denote a rectangle whose shape (i.e., length/width) is (5+sqrt(85))/6.  This rectangle can be partitioned into squares in a manner that matches the continued fraction [2,2,1,2,2,1,...].  It can also be partitioned into rectangles of shape 3/2 and 3 so as to match the continued fraction [5/2, 1, 5/2, 1, ...].  For details, see A188635.

LINKS

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

EXAMPLE

2.369924076215481218333712380293798859541...

MATHEMATICA

FromContinuedFraction[{5/2, 1, {5/2, 1}}]

ContinuedFraction[%, 25]  (* [2, 2, 1, 2, 2, 1, ...] *)

RealDigits[N[%%, 120]]  (* A189967 *)

N[%%%, 40]

RealDigits[(5+Sqrt[85])/6, 10, 120][[1]] (* Harvey P. Dale, Apr 18 2014 *)

PROG

(PARI) (5+sqrt(85))/6 \\ G. C. Greubel, Jan 12 2018

(MAGMA) (5+Sqrt(85))/6 // G. C. Greubel, Jan 12 2018

CROSSREFS

Cf. A188635, A189966.

Sequence in context: A021426 A309008 A249182 * A097108 A140783 A094351

Adjacent sequences:  A189965 A189966 A189967 * A189969 A189970 A189971

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, May 05 2011

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)