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In the '3x+1' problem, take the sequence of starting values which set new records for the highest point of the trajectory before reaching 1 (A006884); sequence gives associated maximal value reached in the trajectory with that start.
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%I #19 Jul 15 2020 12:00:59

%S 2,8,26,80,4616,6560,19682,20762,125252,638468,3405068,4076810,

%T 13557212,25071632,53179010,60506432,296639576,785412368,1241055674,

%U 1399161680,8601188876,12324038948,26241642656,28495741760

%N In the '3x+1' problem, take the sequence of starting values which set new records for the highest point of the trajectory before reaching 1 (A006884); sequence gives associated maximal value reached in the trajectory with that start.

%H David Barina, <a href="/A060410/b060410.txt">Table of n, a(n) for n = 1..93</a> (first 88 terms from the web page of Tomás Oliveira e Silva)

%H David Barina, <a href="http://pcbarina.fit.vutbr.cz/path-records.htm">Path records</a>.

%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>

%Y Cf. A006884, A060409, A060411.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Apr 06 2001