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Search: id:A096485
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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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+0
3
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| 2, 6, 2, 24, 2, 622, 2, 2396, 2, 21912, 2, 527718, 2, 168484, 2, 13171730, 2
(list; graph; listen)
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OFFSET
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2,1
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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 (mathar(AT)strw.leidenuniv.nl), 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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CROSSREFS
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Cf. A002275, A096483, A096484.
Sequence in context: A100892 A126287 A008556 this_sequence A125032 A131980 A076743
Adjacent sequences: A096482 A096483 A096484 this_sequence A096486 A096487 A096488
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KEYWORD
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more,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 24 2004
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