%I A006884 M0843
%S A006884 1,2,3,7,15,27,255,447,639,703,1819,4255,4591,9663,20895,26623,31911,
%T A006884 60975,77671,113383,138367,159487,270271,665215,704511,1042431,1212415,
%U A006884 1441407,1875711,1988859,2643183,2684647,3041127,3873535,4637979,5656191
%N A006884 In the `3x+1' problem, these values for the starting value set new records 
               for highest point of trajectory before reaching 1.
%C A006884 Both the 3x+1 steps and the halving steps are counted.
%D A006884 R. B. Banks, Slicing Pizzas, Racing Turtles and Further Adventues in 
               Applied Mathematics, Princeton Univ. Press, 1999. See p. 96.
%D A006884 B. Hayes, Computer Recreations: On the ups and downs of hailstone numbers, 
               Scientific American, 250 (No. 1, 1984), pp. 10-16.
%D A006884 D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random 
               House, 1980, p. 400.
%D A006884 G. T. Leavens and M. Vermeulen, 3x+1 search problems, Computers and Mathematics 
               with Applications, 24 (1992), 79-99.
%D A006884 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006884 T. D. Noe and N. J. A. Sloane, <a href="b006884.txt">Table of n, a(n) 
               for n=1..89</a> (from Eric Roosendaal's data, supplemented by further 
               values from the web page of Tomas Oliveira e Silva)
%H A006884 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 A006884 Tomas Oliveira e Silva, <a href="http://www.ieeta.pt/~tos/3x+1.html">
               Tables</a> (gives many more terms)
%H A006884 Eric Roosendaal, <a href="http://www.ericr.nl/wondrous/pathrecs.html">
               3x+1 Path Records</a>
%H A006884 <a href="Sindx_3.html#3x1">Index entries for sequences related to 3x+1 
               (or Collatz) problem</a>
%H A006884 <a href="Sindx_Go.html#GEB">Index entries for sequences from "Goedel, 
               Escher, Bach"</a>
%Y A006884 A060409 gives associated "dropping times", A060410 the maximal values 
               and A060411 the steps at which the maxima occur.
%Y A006884 Cf. A006885, A006877, A006878, A033492, A060412-A060415, A132348.
%Y A006884 Sequence in context: A098763 A066044 A066460 this_sequence A074742 A020873 
               A049958
%Y A006884 Adjacent sequences: A006881 A006882 A006883 this_sequence A006885 A006886 
               A006887
%K A006884 nonn,nice,easy
%O A006884 1,2
%A A006884 N. J. A. Sloane (njas(AT)research.att.com), mrob(AT)mrob.com (Robert 
               P Munafo)
%E A006884 b-file extended by N. J. A. Sloane (njas(AT)research.att.com), Nov 27 
               2007