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 A060412 In the `3x+1' problem, these values for the starting value set new records for the "dropping time", number of steps to reach a lower value than the start. 16

%I

%S 2,3,7,27,703,10087,35655,270271,362343,381727,626331,1027431,1126015,

%T 8088063,13421671,20638335,26716671,56924955,63728127,217740015,

%U 1200991791,1827397567,2788008987,12235060455

%N In the `3x+1' problem, these values for the starting value set new records for the "dropping time", number of steps to reach a lower value than the start.

%C The (3x+1)/2 steps and the halving steps are counted. - _Don Reble_, May 13 2006

%C Where records occur in A102419 (could be prefixed by an initial 1). - From _N. J. A. Sloane_, Oct 20 2012

%H N. J. A. Sloane, <a href="/A060412/b060412.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>

%H Eric Roosendaal, <a href="http://www.ericr.nl/wondrous/index.html">On the 3x + 1 problem</a>

%H N. J. A. Sloane, <a href="/A102419/a102419.txt">First 36 terms of A217934 and A060412</a> [From Roosendaal web site]

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

%e See A102419.

%t dcoll[n_]:=Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>=n&]]; t={max=2}; Do[If[(y=dcoll[n])>max,max=y; AppendTo[t,n]],{n,3,1130000,4}]; t (* _Jayanta Basu_, May 28 2013 *)

%Y A060413 gives associated "dropping times", A060414 the maximal values and A060415 the steps at which the maxima occur. See also A217934.

%Y Cf. A060445, A008884, A161021, A161022, A161023, A014682, A126241.

%K nonn

%O 1,1

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

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