OFFSET
1,1
COMMENTS
Decimal expansion of the length/width ratio of a (10/3)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle.
A (10/3)-extension rectangle matches the continued fraction [3,1,1,1,1,3,3,1,1,1,1,3,3,1,1,1,1,3,3,...] for the shape L/W=(5+sqrt(34))/3. 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 (10/3)-extension rectangle, 3 squares are removed first, then 1 square, then 1 square, then 1 square,..., so that the original rectangle of shape (5+sqrt(34))/3 is partitioned into an infinite collection of squares.
EXAMPLE
3.61031729828176682362471762584852769217379944...
MATHEMATICA
r = 10/3; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
RealDigits[(5+Sqrt[34])/3, 10, 140][[1]] (* Harvey P. Dale, Feb 18 2015 *)
PROG
(PARI) (sqrt(34)+5)/3 \\ Charles R Greathouse IV, Apr 25 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 12 2011
STATUS
approved