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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 iterate where maximal value is reached in the trajectory with that start.
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%I #11 Oct 20 2019 21:50:59

%S 0,2,3,4,45,8,31,14,48,28,49,33,26,50,35,43,67,39,69,39,35,124,83,37,

%T 132,46,81,75,83,118,68,42,72,97,98,75,92,199,109,92,92,160,91,197,

%U 119,113,109,124,176,217,234,276,172,164,233,101,109,158,157

%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 iterate where maximal value is reached in the trajectory with that start.

%H N. J. A. Sloane, <a href="/A060411/b060411.txt">Table of n, a(n) for n = 1..88</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>

%Y Cf. A006884, A060409, A060410.

%K nonn

%O 1,2

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