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A006368
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If n even then 3n/2 otherwise nearest integer to 3n/4.
(Formerly M2249)
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16
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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, 20, 42, 22, 45, 23, 48, 25, 51, 26, 54, 28, 57, 29, 60, 31, 63, 32, 66, 34, 69, 35, 72, 37, 75, 38, 78, 40, 81, 41, 84, 43, 87, 44, 90, 46, 93, 47, 96, 49, 99, 50, 102, 52, 105, 53
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| There is a famous open question concerning the trajectory of 8 under this map - see A028393.
Permutation of nonnegative integers: lodumo_3 of A131743. - From DELEHAM Philippe, Oct 24 2011
Multiples of 3 interspersed with numbers other than multiples of 3. [From Harvey P. Dale, Dec 16 2011]
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, E17.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 0..10000
J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see page 5.
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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to 3x+1 (or Collatz) problem
Index entries for two-way infinite sequences
Index entries for sequences that are permutations of the natural numbers
Index to sequences with linear recurrences with constant coefficients, signature (0,1,0,1,0,-1).
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FORMULA
| a(2n)=3n, a(4n+1)=3n+1, a(4n-1)=3n-1. - Michael Somos, Jul 23, 2002
G.f.: x(1+3x+x^2+3x^3+x^4)/((1-x^2)(1-x^4)). - Michael Somos, Jul 23, 2002
a(n)=-a(-n).
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]
a(0)=0, a(1)=1, a(2)=3, a(3)=2, a(4)=6, a(5)=4, a(n)=a(n-2)+a(n-4)- a(n-6) [From Harvey P. Dale, Dec 16 2011]
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EXAMPLE
| 9 is odd so a(9)=round(3*9/4)=round(7-1/4)=7.
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MAPLE
| f:=n-> if n mod 2 = 0 then 3*n/2 elif n mod 4 = 1 then (3*n+1)/4 else (3*n-1)/4; fi; [N. J. A. Sloane, Jan 21 2011]
A006368:=(1+3*z+z**2+3*z**3+z**4)/(1+z**2)/(z-1)**2/(1+z)**2; [Conjectured (correctly, except for the offset) by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[If[EvenQ[n], (3n)/2, Floor[(3n+2)/4]], {n, 0, 80}] (* or *) LinearRecurrence[ {0, 1, 0, 1, 0, -1}, {0, 1, 3, 2, 6, 4}, 80] (* From Harvey P. Dale, Dec 16 2011 *)
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PROG
| (PARI) a(n)=(3*n+n%2)\(2+n%2*2)
(PARI) a(n)=if(n%2, round(3*n/4), 3*n/2)
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CROSSREFS
| Inverse mapping to A006369.
Cf. A028393, A028397, A180853, A180864.
Sequence in context: A191444 A093050 A054089 * A202845 A202838 A105354
Adjacent sequences: A006365 A006366 A006367 * A006369 A006370 A006371
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
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EXTENSIONS
| More terms from Jason Earls (zevi_35711(AT)yahoo.com), Jul 12 2001
Edited by Michael Somos, Jul 23, 2002
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