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A188655
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Decimal expansion of (2+sqrt(13))/3.
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1
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1, 8, 6, 8, 5, 1, 7, 0, 9, 1, 8, 2, 1, 3, 2, 9, 7, 6, 4, 3, 7, 3, 0, 7, 3, 7, 5, 5, 8, 2, 3, 4, 9, 8, 6, 4, 8, 7, 5, 0, 4, 3, 2, 1, 9, 1, 2, 8, 1, 7, 4, 8, 7, 3, 7, 5, 7, 0, 1, 5, 1, 0, 1, 8, 7, 4, 2, 3, 8, 8, 9, 8, 2, 7, 6, 4, 3, 3, 6, 8, 1, 5, 0, 6, 8, 2, 0, 6, 3, 6, 0, 6, 7, 2, 8, 3, 0, 2, 3, 9, 2, 2, 4, 5, 0, 4, 7, 2, 7, 3, 4, 1, 3, 5, 4, 5, 1, 3, 4, 5, 8, 6, 7, 6, 8, 9, 2, 7, 5, 4
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OFFSET
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1,2
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COMMENTS
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Decimal expansion of the length/width ratio of a (4/3)-extension rectangle.
See A188640 for definitions of shape and r-extension rectangle.
A (4/3)-extension rectangle matches the continued fraction [1,1,6,1,1,1,1,6,1,1,1,1,6,...] for the shape L/W= (2+sqrt(13))/3. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,...]. Specifically, for the (4/3)-extension rectangle, 1 square is removed first, then 1 square, then 6 squares, then 1 square, then 1 square,..., so that the original rectangle is partitioned into an infinite collection of squares.
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LINKS
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Table of n, a(n) for n=1..130.
Clark Kimberling, A Visual Euclidean Algorithm, The Mathematics Teacher 76 (1983) 108-109.
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EXAMPLE
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length/width = 1.868517091821329764373....
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MATHEMATICA
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r = 4/3; t = (r + (4 + r^2)^(1/2))/2; RealDigits[ N[ FullSimplify@ t, 111]][[1]]
RealDigits[(2 + Sqrt@ 13)/3, 10, 111][[1]] (* Or *)
RealDigits[Exp@ ArcSinh[2/3], 10, 111][[1]] (* Robert G. Wilson v, Aug 17 2011 *)
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CROSSREFS
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Cf. A188640, A010122.
Sequence in context: A159627 A302682 A011298 * A282152 A191909 A247559
Adjacent sequences: A188652 A188653 A188654 * A188656 A188657 A188658
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KEYWORD
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nonn,cons
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AUTHOR
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Clark Kimberling, Apr 09 2011
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EXTENSIONS
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a(130) corrected by Georg Fischer, Apr 01 2020
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STATUS
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approved
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