A188657 Decimal expansion of (3+sqrt(73))/8.

1, 4, 4, 3, 0, 0, 0, 4, 6, 8, 1, 6, 4, 6, 9, 1, 3, 9, 5, 9, 8, 3, 9, 5, 6, 0, 4, 0, 7, 7, 9, 9, 6, 3, 3, 0, 4, 3, 2, 4, 3, 0, 6, 9, 1, 6, 1, 9, 1, 6, 6, 0, 2, 8, 0, 2, 3, 8, 5, 8, 1, 4, 0, 6, 7, 2, 1, 4, 5, 6, 1, 0, 2, 4, 1, 5, 9, 1, 2, 2, 9, 7, 6, 3, 5, 1, 2, 1, 5, 0, 3, 7, 6, 3, 3, 7, 6, 1, 7, 8, 7, 0, 0, 0, 7, 9, 0, 8, 1, 5, 8

Offset

1,2

Comments

Decimal expansion of the length/width ratio of a (3/4)-extension rectangle.

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

A (3/4)-extension rectangle matches the continued fraction [1,2,3,1,7,1,3,2,1,1,2,3,1,7,1,3,2,...] for the shape L/W= (3+sqrt(73))/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 (3/4)-extension rectangle, 1 square is removed first, then 2 squares, then 3 squares, 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..111.

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

Example

1.4430004681646...

Maple

evalf(3+sqrt(73))/8 ; # R. J. Mathar, Apr 11 2011

Mathematica

RealDigits[(3 + Sqrt[73])/8, 10, 111][[1]] (* Robert G. Wilson v, Aug 19 2011 *)

Prog

(PARI) (sqrt(73)+3)/8 \\ Charles R Greathouse IV, Apr 25 2016

Crossrefs

Cf. A188640, A188656.

Sequence in context: A320147 A369410 A272364 * A021697 A276635 A256845

Adjacent sequences: A188654 A188655 A188656 * A188658 A188659 A188660

Keyword

nonn,cons,easy

Author

Clark Kimberling, Apr 09 2011

Status

approved