Search: id:A006369
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%I A006369 M2245
%S A006369 0,1,3,2,5,7,4,9,11,6,13,15,8,17,19,10,21,23,12,25,27,14,29,31,16,33,35,
%T A006369 18,37,39,20,41,43,22,45,47,24,49,51,26,53,55,28,57,59,30,61,63,32,65,
%U A006369 67,34,69,71,36,73,75,38,77,79,40,81,83,42,85,87,44,89,91,46,93,95
%N A006369 Nearest integer to 4n/3 unless that is an integer, when 2n/3.
%C A006369 This function was studied by Lothar Collatz in 1932.
%C A006369 Fibonacci numbers lodumo 2 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Apr 26 2009]
%C A006369 a(n)=A006368(n)+A168223(n); A168222(n)=a(a(n)); A168221(a(n))=A006368(n). 
               [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 20 
               2009]
%D A006369 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006369 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A006369 R. K. Guy, Unsolved Problems in Number Theory, E17.
%D A006369 M. Klamkin, ed., Problems in Applied Mathematics: Selections from SIAM 
               Review, SIAM, 1990; see pp. 579-581.
%H A006369 R. Zumkeller, <a href="b006369.txt">Table of n, a(n) for n = 0..10000</
               a> [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 
               20 2009]
%H A006369 <a href="Sindx_Tu.html#2wis">Index entries for two-way infinite sequences</
               a>
%H A006369 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 A006369 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 A006369 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 A006369 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%F A006369 G.f.: x(1+3x+2x^2+3x^3+x^4)/(1-x^3)^2. a(3n)=2n, a(3n+1)=4n+1, a(3n-1)=4n-1, 
               a(-n)=-a(n). - Michael Somos, Oct 05 2003
%F A006369 The map is: n -> if n mod 3 = 0 then 2*n/3 elif n mod 3 = 1 then (4*n-1)/
               3 else (4*n+1)/3.
%F A006369 a(n) = (2 - ((2*n + 1) mod 3) mod 2) * floor((2*n + 1)/3) + (2*n + 1) 
               mod 3 - 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jan 23 2005
%F A006369 a(n)=lod_2(F(n)). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 
               26 2009]
%p A006369 A006369 := proc(n) if n mod 3 = 0 then 2*n/3 else round(4*n/3); fi; end;
%p A006369 A006369:=(1+z**2)*(z**2+3*z+1)/(z-1)**2/(z**2+z+1)**2; [Conjectured by 
               S. Plouffe in his 1992 dissertation.]
%o A006369 (PARI) a(n)=if(n%3,round(4*n/3),2*n/3) - Michael Somos, Oct 05 2003
%Y A006369 Inverse mapping to A006368. Cf. A028397, A069196.
%Y A006369 Sequence in context: A128224 A125026 A130295 this_sequence A097284 A105353 
               A115966
%Y A006369 Adjacent sequences: A006366 A006367 A006368 this_sequence A006370 A006371 
               A006372
%K A006369 nonn,nice,easy,new
%O A006369 0,3
%A A006369 N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)

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