This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A181495 #28 Feb 08 2016 11:52:52
%S A181495 1,2,4,10,12,32,36,572,1991,20857,27432,28763,155122,190271,288108,
%T A181495 484709,1395499,9370521,12918396,22646948,49496125,73469408,172128260,
%U A181495 645676547
%N A181495 Positions of the incrementally largest terms in continued fraction for 2^(1/3).
%C A181495 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.
%C A181495 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
%D A181495 H. Davenport, The Higher Arithmetic: An Introduction to the Theory of Numbers, Cambridge, 2008.
%t A181495 Use Max[ContinuedFraction[2^(1/3), n]] for some positive integer n, e.g. Max[ContinuedFraction[2^(1/3), 288108]].
%t A181495 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 *)
%Y A181495 Cf. A002945, A268515.
%K A181495 nonn,more
%O A181495 1,2
%A A181495 _John M. Campbell_, Oct 23 2010
%E A181495 a(19) from _Robert G. Wilson v_, Oct 24 2010
%E A181495 a(20)-a(21) from _Zak Seidov_, Feb 08 2016
%E A181495 a(22)-a(24) from _Hans Havermann_, Feb 08 2016