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.
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
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