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In the '3x+1' problem, take the sequence of starting values which set new records for the "dropping time" (A060412); sequence gives associated maximal value reached in the trajectory with that start.
3

%I #10 Oct 20 2019 21:51:49

%S 2,8,26,4616,125252,1242458,20581856,12324038948,282667562,282667562,

%T 3611141594,8904120362,45119577824,8077577336,795853127168,

%U 44621605808,1848429310544,3604523133626,483308017730

%N In the '3x+1' problem, take the sequence of starting values which set new records for the "dropping time" (A060412); sequence gives associated maximal value reached in the trajectory with that start.

%H N. J. A. Sloane, <a href="/A060414/b060414.txt">Table of n, a(n) for n = 1..35</a> (from the web page of Tomás Oliveira e Silva)

%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/3x+1.html">Tables</a> (gives many more terms)

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Apr 06 2001; b-file added Nov 27 2007