

A188885


Decimal expansion of (1+sqrt(1+e^2))/e.


1



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

1,2


COMMENTS

Decimal expansion of the length/width ratio of a (2/e)extension rectangle. See A188640 for definitions of shape and rextension rectangle.
A (2/e)extension rectangle matches the continued fraction [1,2,3,3,1,15,1,3,7,1,2,4,...] for the shape L/W=(1+sqrt(1+e^2))/e. 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 (2/e)extension rectangle, 1 square is removed first, then 2 squares, then 3 square2, then 3 squares,..., so that the original rectangle of shape (1+sqrt(1+e^2))/e is partitioned into an infinite collection of squares.


LINKS

Table of n, a(n) for n=1..130.


EXAMPLE

1.433400573405154846331906919976752328843391...


MATHEMATICA

r = 2/E; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]


CROSSREFS

Cf. A188640, A188886.
Sequence in context: A282445 A281705 A026858 * A129344 A048853 A303701
Adjacent sequences: A188882 A188883 A188884 * A188886 A188887 A188888


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Apr 12 2011


STATUS

approved



