OFFSET
1,1
COMMENTS
Let R denote a rectangle whose shape (i.e., length/width) is (5+sqrt(85))/6. This rectangle can be partitioned into squares in a manner that matches the continued fraction [2,2,1,2,2,1,...]. It can also be partitioned into rectangles of shape 3/2 and 3 so as to match the continued fraction [5/2, 1, 5/2, 1, ...]. For details, see A188635.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
EXAMPLE
2.369924076215481218333712380293798859541...
MATHEMATICA
FromContinuedFraction[{5/2, 1, {5/2, 1}}]
ContinuedFraction[%, 25] (* [2, 2, 1, 2, 2, 1, ...] *)
RealDigits[N[%%, 120]] (* A189967 *)
N[%%%, 40]
RealDigits[(5+Sqrt[85])/6, 10, 120][[1]] (* Harvey P. Dale, Apr 18 2014 *)
PROG
(PARI) (5+sqrt(85))/6 \\ G. C. Greubel, Jan 12 2018
(Magma) (5+Sqrt(85))/6 // G. C. Greubel, Jan 12 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 05 2011
STATUS
approved