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A059866
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Period length of the continued fraction for sqrt(2^n-1).
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6
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2, 4, 2, 8, 2, 12, 2, 20, 2, 12, 2, 164, 2, 40, 2, 40, 2, 1208, 2, 660, 2, 1304, 2, 3056, 2, 2492, 2, 1080, 2, 13004, 2, 10232, 2, 11296, 2, 148736, 2, 56576, 2, 615482, 2, 44448, 2, 64, 2, 2628524, 2, 28219952, 2, 139558, 2, 3067080, 2, 2683626, 2, 90740360, 2, 103050292, 2
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OFFSET
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2,1
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LINKS
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Chai Wah Wu, Table of n, a(n) for n = 2..78
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EXAMPLE
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For n=7 and n=8 the quotient periods are: [[11], [3, 1, 2, 2, 7, 11, 7, 2, 2, 1, 3, 22]] and [[15], [1, 30]] with period lengths 12 and 2 respectively.
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MAPLE
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with(numtheory): [seq(nops(cfrac(sqrt(2^k-1), 'periodic', 'quotients')[2]), k=2..30)];
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MATHEMATICA
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Table[Length@ Last@ ContinuedFraction[Sqrt[2^n - 1]], {n, 2, 56}] (* Michael De Vlieger, Mar 21 2015 *)
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CROSSREFS
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Cf. A003285, A059926, A059927, A064932.
Sequence in context: A307669 A171977 A266073 * A278262 A093895 A030057
Adjacent sequences: A059863 A059864 A059865 * A059867 A059868 A059869
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Feb 28 2001
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EXTENSIONS
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Corrected and extended by Naohiro Nomoto, Nov 09 2001
a(57)-a(60) from Daniel Suteu, Jan 25 2019
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STATUS
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approved
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