%I A006370 M3198
%S A006370 4,1,10,2,16,3,22,4,28,5,34,6,40,7,46,8,52,9,58,10,64,11,70,12,76,13,
%T A006370 82,14,88,15,94,16,100,17,106,18,112,19,118,20,124,21,130,22,136,23,
%U A006370 142,24,148,25,154,26,160,27,166,28,172,29,178,30,184,31,190,32,196,33
%N A006370 Image of n under the `3x+1' map.
%C A006370 The 3x+1 or Collatz problem is as follows: start with any number n. If 
               n is even, divide it by 2, otherwise multiply it by 3 and add 1. 
               Do we always reach 1? This is an unsolved problem. It is conjectured 
               that the answer is yes.
%C A006370 The Krasikov-Lagarias paper shows that at least N^.84 of the positive 
               numbers <N fall into the 4-2-1 cycle of the 3x+1 problem. This is 
               far short of what we think is true, that all positive numbers fall 
               into this cycle, but it is a step. - Richard Schroeppel, May 01, 
               2002
%D A006370 R. K. Guy, Unsolved Problems in Number Theory, E16.
%D A006370 J. C. Lagarias, The set of rational cycles for the 3x+1 problem, Acta 
               Arithmetica, LVI (1990), pp. 33-53.
%D A006370 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006370 T. D. Noe, <a href="b006370.txt">Table of n, a(n) for n=1..1000</a>
%H A006370 I. Krasikov and J. C. Lagarias, <a href="http://arXiv.org/abs/math.NT/
               0205002">Bounds for the 3x+1 Problem using Difference Inequalities</
               a>
%H A006370 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 A006370 E. Roosendaal, <a href="http://www.ericr.nl/wondrous/index.html">On the 
               3x+1 problem</a>
%H A006370 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A006370 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A006370 <a href="Sindx_3.html#3x1">Index entries for sequences related to 3x+1 
               (or Collatz) problem</a>
%H A006370 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A006370 G.f.: (4x+x^2 +2x^3) / (1-x^2)^2.
%F A006370 a(n)=(1/4)(7n+2-(-1)^n(5n+2)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               May 12 2002
%F A006370 a(n) = ((n mod 2)*2 + 1)*n/(2 - (n mod 2)) + (n mod 2). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Sep 12 2002
%F A006370 a(n)=A014682(n+1)*A000034(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Mar 09 2009]
%p A006370 f := n-> if n mod 2 = 0 then n/2 else 3*n+1; fi;
%p A006370 A006370:=(4+z+2*z**2)/(z-1)**2/(1+z)**2; [S. Plouffe in his 1992 dissertation.]
%o A006370 (PARI) for(n=1,100,print1((1/4)*(7*n+2-(-1)^n*(5*n+2)),","))
%Y A006370 Cf. A139391, A016945, A005408, A016825, A082286.
%Y A006370 Sequence in context: A059926 A138775 A121529 this_sequence A108759 A158824 
               A039806
%Y A006370 Adjacent sequences: A006367 A006368 A006369 this_sequence A006371 A006372 
               A006373
%K A006370 nonn,nice
%O A006370 1,1
%A A006370 N. J. A. Sloane (njas(AT)research.att.com).
%E A006370 More terms from Larry Reeves (larryr(AT)acm.org), Apr 27 2001