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A181495
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Positions of the incrementally largest terms in continued fraction for 2^(1/3).
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2
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1, 2, 4, 10, 12, 32, 36, 572, 1991, 20857, 27432, 28763, 155122, 190271, 288108, 484709, 1395499, 9370521, 12918396, 22646948, 49496125, 73469408, 172128260, 645676547
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OFFSET
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1,2
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COMMENTS
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The corresponding records (or high-water marks) in A002945, the continued fraction for 2^(1/3), are {1, 3, 5, 8, 14, 15, 534, 7451, 12737, 22466, 68346, 148017, 217441, 320408, 533679, 4156269, 4886972, 10253793, ...} - see A268515.
It is not known if this sequence is infinite (i.e., whether the continued fraction expansion is bounded). [Davenport]. - N. J. A. Sloane, Feb 07 2016
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REFERENCES
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H. Davenport, The Higher Arithmetic: An Introduction to the Theory of Numbers, Cambridge, 2008.
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LINKS
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MATHEMATICA
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Use Max[ContinuedFraction[2^(1/3), n]] for some positive integer n, e.g. Max[ContinuedFraction[2^(1/3), 288108]].
cf = ContinuedFraction[2^(1/3), 20000000]; mx = 0; k = 1; lst = {}; While[k < 20000000, If[ cf[[k]] > mx, mx = cf[[k]]; AppendTo[lst, k]; Print[{k, cf[[k]]}]]; k++ ]; lst (* Robert G. Wilson v, Oct 24 2010 *)
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CROSSREFS
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KEYWORD
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nonn,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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