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

Offset: 1

Author

Clark Kimberling, Apr 15 2011

Keywords

• nonn
• cons
• easy

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.

Examples

			2.2796103731105126266020168769161733623002084362...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A188738, A189040, A189041.

Programs

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 *)

Extensions

Corrected by Harvey P. Dale, Oct 17 2013