A189966 -id:A189966 - cp's OEIS frontend

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, 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

Offset: 1

Clark Kimberling, May 05 2011

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.

			2.369924076215481218333712380293798859541...

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

Cf. A188635, A189966.

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

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 *)

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

cp's OEIS Frontend

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, ...].

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