A188658 Decimal expansion of (1+sqrt(101))/10.

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

Offset: 1

Author

Clark Kimberling, Apr 10 2011

Keywords

• nonn
• cons

Comments

Decimal expansion of the shape of a (1/5)-extension rectangle; see A188640 for definitions of shape and r-extension rectangle. Briefly, shape=length/width, and an r-extension rectangle is composed of two rectangles of shape 1/r when r<1.

The continued fraction is 1, 9, 1, 1, 9, 1, 1, 9, 1, 1, 9, 1, 1, 9, 1...

Examples

			1.104987562112089027021926491275957618694502347002...
		

Links

• Clark Kimberling, A Visual Euclidean Algorithm, The Mathematics Teacher 76 (1983) 108-109.

Crossrefs

Cf. A188640.

Programs

Mathematica

r = 1/5; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
RealDigits[(1+Sqrt[101])/10,10,150][[1]] (* Harvey P. Dale, Nov 29 2020 *)

Formula

Equals exp(arcsinh(1/10)). - Amiram Eldar, Jul 04 2023

Extensions

a(130) corrected by Georg Fischer, Apr 02 2020