%I A005186 M0305
%S A005186 1,1,1,1,1,2,2,4,4,6,6,8,10,14,18,24,29,36,44,58,72,91,113,143,179,227,
%T A005186 287,366,460,578,732,926,1174,1489,1879,2365,2988,3780,4788,6049,7628,
%U A005186 9635,12190,15409,19452,24561,31025,39229,49580,62680,79255,100144
%N A005186 a(n) = number of m which take n steps to reach 1 in `3x+1' problem.
%D A005186 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005186 S. N. Anderson, Struggling with the 3x+1 problem, Math. Gazette, 71 (1987), 
               271-274.
%D A005186 R. K. Guy, personal communication.
%H A005186 T. D. Noe, <a href="b005186.txt">Table of n, a(n) for n=0..70</a>
%H A005186 <a href="Sindx_3.html#3x1">Index entries for sequences related to 3x+1 
               (or Collatz) problem</a>
%F A005186 Appears to settle into approximately exponential growth after about 25 
               terms or so, with a ratio between adjacent terms of roughly 1.264. 
               - Howard A. Landman (howard(AT)riverrock.org), May 24 2003
%F A005186 David W. Wilson (Jun 10, 2003) gives a heuristic argument that the constant 
               should be the largest eigenvalue of the matrix [ 1 0 0 1 0 0 / 0 
               0 0 0 1/3 0 / 0 1 0 0 1 0 / 0 0 0 0 1/3 0 / 0 0 1 0 0 1 / 0 0 0 0 
               1/3 0 ], which is (3 + sqrt(21))/6 = 1.2637626...
%o A005186 #!/usr/bin/perl @old = ( 1 ); while (1) { print scalar(@old), " "; @new 
               = ( ); foreach $n (@old) { $used{$n} = 1; if (($n % 6) == 4) { $m 
               = ($n-1)/3; push(@new,$m) unless ($used{$m}); } $m = $n + $n; push(@new,
               $m) unless ($used{$m}); } @old = @new; }
%Y A005186 Cf. A088975
%Y A005186 Sequence in context: A131055 A052928 A137501 this_sequence A008642 A001364 
               A029010
%Y A005186 Adjacent sequences: A005183 A005184 A005185 this_sequence A005187 A005188 
               A005189
%K A005186 nonn,easy,nice
%O A005186 0,6
%A A005186 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
%E A005186 More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001