Search: id:A006368
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%I A006368 M2249
%S A006368 0,1,3,2,6,4,9,5,12,7,15,8,18,10,21,11,24,13,27,14,30,16,33,17,36,19,39,
%T A006368 20,42,22,45,23,48,25,51,26,54,28,57,29,60,31,63,32,66,34,69,35,72,37,
%U A006368 75,38,78,40,81,41,84,43,87,44,90,46,93,47,96,49,99,50,102,52,105,53
%N A006368 If n even then 3n/2 otherwise nearest integer to 3n/4.
%C A006368 a(n)=-a(-n).
%C A006368 a(n)=A006369(n)-A168223(n); A168221(n)=a(a(n)); A168222(a(n))=A006369(n). 
               [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 20 
               2009]
%D A006368 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006368 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 A006368 R. K. Guy, Unsolved Problems in Number Theory, E17.
%H A006368 R. Zumkeller, <a href="b006368.txt">Table of n, a(n) for n = 0..10000</
               a> [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 
               20 2009]
%H A006368 <a href="Sindx_Tu.html#2wis">Index entries for two-way infinite sequences</
               a>
%H A006368 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 A006368 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 A006368 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%F A006368 G.f.: x(1+3x+x^2+3x^3+x^4)/((1-x^2)(1-x^4)). a(2n)=3n, a(4n+1)=3n+1, 
               a(4n-1)=3n-1. - Michael Somos, Jul 23, 2002
%e A006368 9 is odd so a(9)=round(3*9/4)=round(7-1/4)=7.
%p A006368 A006368:=(1+3*z+z**2+3*z**3+z**4)/(1+z**2)/(z-1)**2/(1+z)**2; [Conjectured 
               by S. Plouffe in his 1992 dissertation.]
%o A006368 (PARI) a(n)=(3*n+n%2)\(2+n%2*2)
%o A006368 (PARI) a(n)=if(n%2,round(3*n/4),3*n/2)
%Y A006368 Inverse mapping to A006369.
%Y A006368 Cf. A028397.
%Y A006368 Sequence in context: A064789 A093050 A054089 this_sequence A105354 A094077 
               A091018
%Y A006368 Adjacent sequences: A006365 A006366 A006367 this_sequence A006369 A006370 
               A006371
%K A006368 nonn,nice,easy,new
%O A006368 0,3
%A A006368 N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
%E A006368 More terms from Jason Earls (zevi_35711(AT)yahoo.com), Jul 12 2001
%E A006368 Edited by Michael Somos, Jul 23, 2002

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