A188736 Decimal expansion of (3+sqrt(34))/5.

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

Offset

1,2

Comments

Decimal expansion of the length/width ratio of a (6/5)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle.

A (6/5)-extension rectangle matches the continued fraction [1,1,3,3,1,1,1,1,3,3,1,1,1,1,3,3,...] for the shape L/W=(3+sqrt(34))/5. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,1,...]. Specifically, for the (6/5)-extension rectangle, 1 square is removed first, then 1 square, then 3 squares, then 3 squares,..., so that the original rectangle of shape (3+sqrt(34))/5 is partitioned into an infinite collection of squares.

Links

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

Example

1.76619037896906009417483057550911661530...

Maple

evalf((3+sqrt(34))/5, 140); # Muniru A Asiru, Nov 01 2018

Mathematica

RealDigits[(3 + Sqrt[34])/5, 10, 111][[1]] (* Robert G. Wilson v, Aug 18 2011 *)

Prog

(PARI) (sqrt(34)+3)/5 \\ Charles R Greathouse IV, Apr 25 2016
(Magma) SetDefaultRealField(RealField(100)); (3 + Sqrt(34))/5; // G. C. Greubel, Nov 01 2018

Crossrefs

Cf. A188640.

Sequence in context: A198109 A059751 A019859 * A265304 A102769 A031348

Adjacent sequences: A188733 A188734 A188735 * A188737 A188738 A188739

Keyword

nonn,cons

Author

Clark Kimberling, Apr 12 2011

Status

approved