OFFSET
1,1
COMMENTS
The rectangle R whose shape (i.e., length/width) is (15+sqrt(465))/12 can be partitioned into rectangles of shapes 5/2 and 3/2 in a manner that matches the periodic continued fraction [5/2, 3/2, 5/2, 3/2,...]. R can also be partitioned into squares so as to match the periodic continued fraction [3,21,3,1,1,4,1,4,1,1,3,21,...]. For details, see A188635.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
EXAMPLE
3.046988221070652056227828483250098729807...
MATHEMATICA
FromContinuedFraction[{5/2, 3/2, {5/2, 3/2}}]
FullSimplify[%]
ContinuedFraction[%, 100] (* [3, 21, 3, 1, 1, 4, 1, 4, 1, 1, 3, 21, ...] *)
RealDigits[N[%%, 120]] (* A190181 *)
N[%%%, 40]
RealDigits[(15+Sqrt[465])/12, 10, 100][[1]] (* G. C. Greubel, Dec 28 2017 *)
PROG
(PARI) (15+sqrt(465))/12 \\ G. C. Greubel, Dec 28 2017
(Magma) [(15+sqrt(465))/12]; // G. C. Greubel, Dec 28 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 05 2011
STATUS
approved