OFFSET
0,1
COMMENTS
This is the most natural example of the fact that the sum of two periodic continued fractions need not have a periodic continued fraction.
a(n) is the numbers of squares removed at stage n of the continued-fraction partitioning of a rectangle of length L and width W satisfying W=L*sqrt(8); see A188640. - Clark Kimberling, Apr 13 2011
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
G. Xiao, Contfrac
MATHEMATICA
r = 8^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
ContinuedFraction[Sqrt[2]+Sqrt[3], 100] (* Harvey P. Dale, Aug 17 2019 *)
PROG
(PARI) contfrac(sqrt(2)+sqrt(3)) \\ Michel Marcus, Mar 12 2017
CROSSREFS
KEYWORD
cofr,nonn
AUTHOR
Jeppe Stig Nielsen, Dec 04 2003
STATUS
approved