A188941 Decimal expansion of (9+sqrt(65))/4.

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

Offset: 1

Author

Clark Kimberling, Apr 14 2011

Keywords

• nonn
• cons

Comments

Apart from the first digit, the same as A171417. Apart from the first 2 digits, the same as A188734. - R. J. Mathar, Apr 15 2011

Decimal expansion of the shape (= length/width = (9+sqrt(65))/4) of the greater (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

			4.2655644370746374130916533075759427827835990...
		

Crossrefs

Cf. A188738, A188940.

Programs

Mathematica

r = 9/2; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
RealDigits[(9+Sqrt[65])/4,10,150][[1]] (* Harvey P. Dale, Jan 31 2023 *)

PARI

(9+sqrt(65))/4 \\ Jinyuan Wang, Apr 14 2020