A188940 Decimal expansion of (9-sqrt(65))/4.

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

Offset: 1

Author

Clark Kimberling, Apr 14 2011

Keywords

• nonn
• cons
• easy

Comments

Decimal expansion of the shape (= length/width = (9-sqrt(65))/4) of the lesser (9/2)-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

			0.23443556292536258690834669242405721721640...
		

Crossrefs

Cf. A188941, A188738.

Programs

Mathematica

r = 9/2; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]