OFFSET
1,2
COMMENTS
Decimal expansion of shape of an (e/2)-extension rectangle; see A188640 for definitions of shape and r-extension rectangle. Briefly, an r-extension rectangle is composed of two rectangles of shape r.
An (e/2)-extension rectangle matches the continued fraction A188728 of the shape L/W = (r+sqrt(4+r^2))/2. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,...]. Specifically, for an (e/2)-extension rectangle, 1 square is removed first, then 1 square, then 7 squares, then 1 square, then 46 squares,..., so that the original rectangle is partitioned into an infinite collection of squares.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
EXAMPLE
1.88862628964821616707581942532177092442419527...
MAPLE
evalf((exp(1)+sqrt(16+exp(2)))/4, 140); # Muniru A Asiru, Nov 01 2018
MATHEMATICA
PROG
(PARI) default(realprecision, 100); (exp(1) + sqrt(16 + exp(2)))/4 \\ G. C. Greubel, Oct 31 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (Exp(1) + Sqrt(16 + Exp(2)))/4; // G. C. Greubel, Oct 31 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 10 2011
STATUS
approved