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
Programs
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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