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 A365478 #35 Sep 25 2023 18:22:33 %S A365478 1,2,8,4,8,8,26,8,26,10,26,12,20,26,80,16,26,26,44,20,32,26,80,24,44, %T A365478 26,4616,28,44,80,4616,32,50,34,80,36,56,44,152,40,4616,42,98,44,68, %U A365478 80,4616,48,74,50,116,52,80,4616,4616,56,98,58,152,80,92,4616,4616 %N A365478 In the Collatz problem, largest value in the trajectory of n in the 3x+1 function (denoted by T(x) in the literature, and defined as T(x) = (3x+1)/2 if x is odd, T(x) = x/2 if x is even), or -1 if the trajectory is divergent. %C A365478 This sequence differs from A025586, where the division by 2 does not immediately follow the 3x+1 step when x is odd. %C A365478 Here by definition the trajectory ends when 1 is reached, so a(1) = 1. %C A365478 Kontorovich and Lagarias (2009, 2010) call these values the maximum excursion values. %H A365478 Paolo Xausa, <a href="/A365478/b365478.txt">Table of n, a(n) for n = 1..10000</a> %H A365478 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 A365478 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a> %F A365478 a(n) <= A025586(n). %e A365478 a(11) = 26 because 26 is the largest value in the trajectory 11 -> 17 -> 26 -> 13 -> 20 -> 10 -> 5 -> 8 -> 4 -> 2 -> 1. %t A365478 A365478[n_]:=Max[NestWhileList[If[OddQ[#],(3#+1)/2,#/2]&,n,#>1&]];Array[A365478,100] %Y A365478 Cf. A014682, A025586 (equivalent for the Collatz function), A166245. %K A365478 nonn %O A365478 1,2 %A A365478 _Paolo Xausa_, Sep 05 2023