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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 "dropping time", number of steps to reach a lower value than the start.
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%I #11 Oct 20 2019 21:50:40

%S 1,4,7,7,59,13,40,23,81,61,70,65,54,72,65,59,127,105,110,59,72,164,

%T 140,73,170,105,149,97,135,183,99,99,124,156,200,140,222,264,181,243,

%U 203,238,262,362,249,183,238,226,243,294,375,455,292,245,414

%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 "dropping time", number of steps to reach a lower value than the start.

%H N. J. A. Sloane, <a href="/A060409/b060409.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, A060410, A060411.

%K nonn

%O 1,2

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