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A096485
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Period length of continued fraction for square root of n-th decimal repunit.
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3
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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
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OFFSET
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2,1
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LINKS
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EXAMPLE
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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.
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MAPLE
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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)];
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MATHEMATICA
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Do[Print[Length[Last[ContinuedFraction[((-1+10^n)/9)^(1/2)]]]], {n, 2, 18}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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