A189042 Decimal expansion of (e-sqrt(-4+e^2))/2.

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

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

Table of n, a(n) for n=0..129.

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

Cf. A188738, A189040, A189041.

Sequence in context: A007015 A354139 A114562 * A011451 A200089 A330686

Adjacent sequences: A189039 A189040 A189041 * A189043 A189044 A189045

Keyword

nonn,cons

Author

Clark Kimberling, Apr 15 2011

Extensions

a(129) corrected by Georg Fischer, Apr 04 2020

Status

approved