A188943 Decimal expansion of (7 + sqrt(13))/6.

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

Offset: 1

Author

Clark Kimberling, Apr 14 2011

Keywords

• nonn
• cons

Comments

Decimal expansion of the shape (= length/width = (7+sqrt(13))/6) of the greater (7/3)-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.

From Wolfdieter Lang, Aug 29 2022: (Start)

This constant t is an element of the quadratic number field Q(sqrt(13)) with (monic) polynomial x^2 - (7/3)*x + 1, and the negative root is -A188942.

The constant t - 1 = (1 + sqrt(13))/6 = A209927/3 has minimal polynomial x^2 - x/3 - 1/3, with negative root -(-1 + sqrt(13))/6 = -A223139/3 = -A356033.

(End)

Examples

			1.7675918792439982155198702112450826577085494289742...
		

Crossrefs

Cf. A188738, A188942, A209927, A223139, A356033.

Programs

Mathematica

r = 7/3; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]