%I A006666 M3733
%S A006666 0,1,5,2,4,6,11,3,13,5,10,7,7,12,12,4,9,14,14,6,6,11,11,8,16,8,70,13,
%T A006666 13,13,67,5,18,10,10,15,15,15,23,7,69,7,20,12,12,12,66,9,17,17,17,9,9,
%U A006666 71,71,14,22,14,22,14,14,68,68,6,19,19,19,11,11,11,65,16,73,16,11,16
%N A006666 Number of halving steps to reach 1 in `3x+1' problem.
%C A006666 Equals the total number of steps to reach 1 under the modified `3x+1' 
               map: n -> n/2 if n is even, n -> (3n+1)/2 if n is odd.
%D A006666 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006666 R. K. Guy, Unsolved Problems in Number Theory, E16.
%H A006666 T. D. Noe, <a href="b006666.txt">Table of n, a(n) for n=1..10000</a>
%H A006666 J. C. Lagarias, <a href="http://www.cecm.sfu.ca/organics/papers/lagarias/
               paper/html/paper.html">The 3x+1 problem and its generalizations</
               a>, Amer. Math. Monthly, 92 (1985), 3-23.
%H A006666 K. Matthews, <a href="http://www.numbertheory.org/php/collatz.html">The 
               Collatz Conjecture</a>
%H A006666 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CollatzProblem.html">Collatz Problem</a>
%H A006666 <a href="Sindx_3.html#3x1">Index entries for sequences related to 3x+1 
               (or Collatz) problem</a>
%e A006666 2->1 so a(2) = 1; 3->10->5->16->8->4->2->1, with 5 halving steps, so 
               a(3) = 5; 4->2->1 has two halving steps, so a(4) = 2; etc.
%Y A006666 Sequence in context: A021660 A064853 A112597 this_sequence A163334 A029683 
               A063567
%Y A006666 Adjacent sequences: A006663 A006664 A006665 this_sequence A006667 A006668 
               A006669
%K A006666 nonn,nice
%O A006666 1,3
%A A006666 N. J. A. Sloane (njas(AT)research.att.com), R. W. Gosper
%E A006666 More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001