OFFSET
2,1
EXAMPLE
n=10: the period is [3,66666];
n=3: the period is [2, 2, 4, 5, 2, 7, 1, 41, 3, 1, 1, 4, 1, 1, 3, 41, 1, 7, 2, 5, 4, 2, 2, 210], 24 terms.
MAPLE
A096485 := proc(n) ((10^n-1)/9)^(1/2) ; nops(numtheory[cfrac](%, 'periodic', 'quotients')[2]) ; end: for n from 2 to 10 do print(A096485(n)) ; od ; # R. J. Mathar, Apr 30 2007
with(numtheory): [seq(nops(cfrac(((10^k-1/9)^(1/2), 'periodic', 'quotients')[2]), k=2..10)];
MATHEMATICA
Do[Print[Length[Last[ContinuedFraction[((-1+10^n)/9)^(1/2)]]]], {n, 2, 18}]
PROG
(Python)
from sympy.ntheory.continued_fraction import continued_fraction
from sympy import sqrt
def A096485(n): return len(continued_fraction(sqrt((10**n-1)//9))[-1]) # Chai Wah Wu, Mar 30 2021
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Labos Elemer, Jun 24 2004
EXTENSIONS
a(19)-a(26) from Hiroaki Yamanouchi, Oct 17 2015
a(27)-a(28) from Chai Wah Wu, Sep 14 2021
STATUS
approved