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 A181495 Positions of the incrementally largest terms in continued fraction for 2^(1/3). 2
 1, 2, 4, 10, 12, 32, 36, 572, 1991, 20857, 27432, 28763, 155122, 190271, 288108, 484709, 1395499, 9370521, 12918396, 22646948, 49496125, 73469408, 172128260, 645676547 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 REFERENCES H. Davenport, The Higher Arithmetic: An Introduction to the Theory of Numbers, Cambridge, 2008. LINKS Table of n, a(n) for n=1..24. MATHEMATICA 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 *) CROSSREFS Cf. A002945, A268515. Sequence in context: A034166 A301338 A364667 * A092367 A366773 A216814 Adjacent sequences: A181492 A181493 A181494 * A181496 A181497 A181498 KEYWORD nonn,more AUTHOR John M. Campbell, Oct 23 2010 EXTENSIONS a(19) from Robert G. Wilson v, Oct 24 2010 a(20)-a(21) from Zak Seidov, Feb 08 2016 a(22)-a(24) from Hans Havermann, Feb 08 2016 STATUS approved

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Last modified September 11 17:54 EDT 2024. Contains 375839 sequences. (Running on oeis4.)