cp's OEIS Frontend

A365482 In the Collatz (3x+1) problem, values in A006884 for which the maximum excursion ratio (see comments) is greater than 2.

%I A365482 #26 Oct 08 2023 21:17:51
%S A365482 27,319804831,1410123943,3716509988199,9016346070511,1254251874774375,
%T A365482 10709980568908647,1980976057694848447
%N A365482 In the Collatz (3x+1) problem, values in A006884 for which the maximum excursion ratio (see comments) is greater than 2.
%C A365482 Kontorovich and Lagarias (2009, 2010) define the maximum excursion ratio as the ratio between the log of the highest point in the trajectory of the T function (started at x) and the log of x, where T(x) is the 3x+1 function = (3x+1)/2 if x is odd, x/2 if x is even (A014682).
%C A365482 They use data from Oliveira e Silva (2010) to compile Table 3 in their paper, but they omit the a(7) = 10709980568908647 value (cf. also Barina and Roosendall links).
%C A365482 Equivalently, values in A006884 for which A365478(A006884(k)) / A006884(k)^2 > 1, for k >= 1.
%C A365482 See A365483 for corresponding maximum excursion values.
%H A365482 David Barina, <a href="http://pcbarina.fit.vutbr.cz/path-records.htm">Path records</a>.
%H A365482 Alex V. Kontorovich and Jeffrey C. Lagarias, <a href="https://arxiv.org/abs/0910.1944">Stochastic Models for the 3x+1 and 5x+1 Problems</a>, arXiv:0910.1944 [math.NT], 2009, pp. 11-14, and in Jeffrey C. Lagarias, ed., <a href="http://www.ams.org/bookstore-getitem/item=mbk-78">The Ultimate Challenge: The 3x+1 Problem</a>, American Mathematical Society, 2010, pp. 140-142.
%H A365482 Tomás Oliveira e Silva, Empirical Verification of the 3x+1 and Related Conjectures, in Jeffrey C. Lagarias, ed., <a href="http://www.ams.org/bookstore-getitem/item=mbk-78">The Ultimate Challenge: The 3x+1 Problem</a>, American Mathematical Society, 2010, pp. 189-207.
%H A365482 Eric Roosendall, <a href="http://ericr.nl/wondrous/pathrecs.html">3x + 1 Path Records</a>.
%H A365482 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%Y A365482 Subsequence of A006884.
%Y A365482 Cf. A014682, A365478, A365483.
%K A365482 nonn,hard,more
%O A365482 1,1
%A A365482 _Paolo Xausa_, Sep 05 2023