A096485 Period length of continued fraction for square root of n-th decimal repunit.

2, 6, 2, 24, 2, 622, 2, 2396, 2, 21912, 2, 527718, 2, 168484, 2, 13171730, 2, 359947864, 2, 52090778, 2, 16658818532, 2, 134257065348, 2, 61403998114, 2

Offset: 2

Author

Labos Elemer, Jun 24 2004

Keywords

• nonn
• base
• more

Examples

			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.
		

Crossrefs

Cf. A002275, A096483, A096484.

Programs

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}]

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

Extensions

a(19)-a(26) from Hiroaki Yamanouchi, Oct 17 2015

a(27)-a(28) from Chai Wah Wu, Sep 14 2021