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A190290 Decimal expansion of (3+sqrt(21))/3. 2
2, 5, 2, 7, 5, 2, 5, 2, 3, 1, 6, 5, 1, 9, 4, 6, 6, 6, 8, 8, 6, 2, 6, 8, 2, 3, 9, 7, 9, 0, 9, 3, 3, 6, 1, 6, 2, 9, 9, 4, 8, 1, 8, 8, 5, 8, 9, 2, 2, 6, 5, 7, 3, 0, 0, 8, 6, 9, 0, 8, 0, 7, 0, 7, 9, 6, 8, 9, 5, 6, 1, 4, 1, 8, 4, 9, 2, 5, 6, 9, 6, 2, 2, 0, 1, 4, 5, 3, 8, 5, 3, 1, 6, 4, 4, 8, 1, 6, 7, 7, 5, 5, 9, 2, 0, 0, 3, 0, 1, 7, 9, 9, 1, 9, 5, 2, 4, 6, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The rectangle R whose shape (i.e., length/width) is (3+sqrt(21))/3, can be partitioned into rectangles of shapes 3/2 and 2 in a manner that matches the periodic continued fraction [2, 3/2, 2, 3/2, ...].  R can also be partitioned into squares so as to match the periodic continued fraction [2,1,1,8,1,1,2,1,1,8,1,1,2,,...].  For details, see A188635.

LINKS

Table of n, a(n) for n=1..120.

EXAMPLE

2.527525231651946668862682397909336162995...

MATHEMATICA

FromContinuedFraction[{2, 3/2, {2, 3/2}}]

ContinuedFraction[%, 100]  (* [2, 1, 1, 8, 1, 1, 2, ... *)

RealDigits[N[%%, 120]]     (* A190290 *)

N[%%%, 40]

CROSSREFS

Cf. A188635, A190289.

Sequence in context: A142583 A086956 A198570 * A246341 A246355 A016580

Adjacent sequences:  A190287 A190288 A190289 * A190291 A190292 A190293

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, May 07 2011

STATUS

approved

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Last modified May 24 20:53 EDT 2019. Contains 323534 sequences. (Running on oeis4.)