A189040 - OEIS

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A189040

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

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

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OFFSET

1,1

COMMENTS

Decimal expansion of the shape (= length/width = ((e+sqrt(-4+e^2))/2) of the greater 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=1..86.

Index entries for transcendental numbers

EXAMPLE

2.2796103731105126266020168769161733623002084362...

MATHEMATICA

r = E; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]

N[t, 130]

RealDigits[N[t, 130]][[1]]

ContinuedFraction[t, 120]

RealDigits[(E+Sqrt[E^2-4])/2, 10, 150][[1]] (* Harvey P. Dale, Oct 17 2013 *)

CROSSREFS