OFFSET
1,4
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...
LINKS
Clark Kimberling, A Visual Euclidean Algorithm, The Mathematics Teacher 76 (1983) 108-109.
FORMULA
Equals exp(arcsinh(1/10)). - Amiram Eldar, Jul 04 2023
EXAMPLE
1.104987562112089027021926491275957618694502347002...
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 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 10 2011
EXTENSIONS
a(130) corrected by Georg Fischer, Apr 02 2020
STATUS
approved