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
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 12 2011
STATUS
approved