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A189042 Decimal expansion of (e-sqrt(-4+e^2))/2. 0
4, 3, 8, 6, 7, 1, 4, 5, 5, 3, 4, 8, 5, 3, 2, 6, 0, 8, 7, 5, 8, 2, 7, 0, 5, 9, 4, 4, 3, 6, 4, 8, 9, 1, 3, 5, 4, 5, 7, 0, 3, 8, 6, 5, 7, 4, 7, 1, 4, 3, 9, 4, 3, 6, 7, 4, 8, 8, 7, 5, 5, 6, 1, 0, 1, 7, 0, 8, 8, 7, 6, 8, 1, 7, 5, 1, 8, 0, 7, 8, 5, 4, 4, 7, 0, 4, 5, 3, 4, 2, 1, 1, 1, 8, 4, 6, 4, 8, 2, 8, 1, 0, 3, 0, 9, 6, 8, 6, 0, 0, 5, 0, 4, 3, 7, 1, 7, 4, 8, 2, 3, 1, 6, 1, 1, 2, 2, 1, 2, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Decimal expansion of the shape (= length/width = (e-sqrt(-4+e^2))/2) of the lesser e-contraction rectangle.
See A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and partitioning these rectangles into a sets of squares in a manner that matches the continued fractions of their shapes.
LINKS
EXAMPLE
0.4386714553485326087582705944364891354570...
MATHEMATICA
r = E; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
PROG
(PARI) (exp(1)-sqrt(exp(2)-4))/2 \\ Charles R Greathouse IV, Apr 25 2016
CROSSREFS
Sequence in context: A007015 A354139 A114562 * A011451 A200089 A330686
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 15 2011
EXTENSIONS
a(129) corrected by Georg Fischer, Apr 04 2020
STATUS
approved

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Last modified April 12 09:28 EDT 2024. Contains 371627 sequences. (Running on oeis4.)