OFFSET
1,1
COMMENTS
Decimal expansion of the length/width ratio of a (7/3)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle.
A (7/3)-extension rectangle matches the continued fraction [2,1,2,2,1,2,2,1,2,2,1,...] for the shape L/W=(7+sqrt(85))/6. 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 (7/3)-extension rectangle, 2 squares are removed first, then 1 square, then 2 squares, then 2 squares,..., so that the original rectangle of shape (7+sqrt(85))/6 is partitioned into an infinite collection of squares.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
EXAMPLE
2.703257409548814551667045713627132192874467508120...
MAPLE
evalf((7+sqrt(85))/6, 140); # Muniru A Asiru, Nov 01 2018
MATHEMATICA
r = 7/3; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
PROG
(PARI) default(realprecision, 100); (7+sqrt(85))/6 \\ G. C. Greubel, Nov 01 2018
(Magma) SetDefaultRealField(RealField(100)); (7+Sqrt(85))/6; // G. C. Greubel, Nov 01 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 12 2011
STATUS
approved