A096488 Number of different terms in a period of continued fraction for square root of n-th repunit.

2, 3, 2, 8, 2, 37, 2, 76, 2, 217, 2, 870, 2, 583, 2, 5034, 2, 28494, 2, 10058, 2, 187966, 2, 383291, 2, 340992, 2

Offset: 2

Author

Labos Elemer, Jun 25 2004

Keywords

• nonn
• more

Crossrefs

Cf. A002275, A096485, A096487.

Programs

Mathematica

Do[Print[Length[Union[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 A096488(n): return len(set(continued_fraction(sqrt((10**n-1)//9))[-1])) # Chai Wah Wu, Mar 30 2021

Extensions

Name edited by Michel Marcus, Aug 22 2019

a(19)-a(22) from Daniel Suteu, Aug 22 2019

a(23)-a(28) from Chai Wah Wu, Apr 05 2021