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A188656 Decimal expansion of (1+sqrt(65))/8. 2
1, 1, 3, 2, 7, 8, 2, 2, 1, 8, 5, 3, 7, 3, 1, 8, 7, 0, 6, 5, 4, 5, 8, 2, 6, 6, 5, 3, 7, 8, 7, 9, 7, 1, 3, 9, 1, 3, 9, 1, 7, 9, 9, 5, 3, 8, 2, 0, 1, 0, 7, 1, 6, 7, 3, 4, 9, 2, 0, 7, 4, 0, 4, 8, 6, 5, 7, 9, 8, 4, 3, 6, 8, 8, 7, 8, 2, 1, 1, 0, 2, 5, 3, 7, 0, 0, 1, 9, 2, 8, 3, 3, 3, 9, 6, 5, 3, 8, 3, 0, 4, 5, 4, 6, 8, 0, 3, 0, 8, 2, 6, 7, 4, 9, 3, 2, 3, 9, 0, 2, 6, 7, 1, 8, 5, 8, 1, 5, 1, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Apart from the second digit the same as A177707.

Decimal expansion of the shape of a (1/4)-extension rectangle.

See A188640 for definitions of shape and r-extension rectangle.

A (1/4)-extension rectangle matches the continued fraction [1,7,1,1,7,1,1,7,1,1,7,1,1,7,...] for the shape L/W= (1+sqrt(65))/8.  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 7 squares, then 1 square, then 1 square, then 7 squares,..., so that the original rectangle is partitioned into an infinite collection of squares.

LINKS

Table of n, a(n) for n=1..130.

Clark Kimberling, A Visual Euclidean Algorithm, The Mathematics Teacher 76 (1983) 108-109.

EXAMPLE

length/width = 1.13278221853731870654582665....

MATHEMATICA

RealDigits[(1 + Sqrt[65])/8, 10, 111][[1]] (* Robert G. Wilson v, Aug 19 2011 *)

CROSSREFS

Cf. A188640, A105395.

Sequence in context: A324876 A226370 A054183 * A210204 A208657 A329940

Adjacent sequences:  A188653 A188654 A188655 * A188657 A188658 A188659

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Apr 09 2011

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)