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Search: id:A007494
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| A007494 |
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Congruent to 0 or 2 mod 3. |
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+0
12
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| 0, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102, 104, 105, 107
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The map n -> a(n) (where a(n) = 3n/2 if n even or (3n+1)/2 if n odd) was studied by Mahler, in connection with "Z-numbers", and later by Flatto. One question was whether, iterating from an initial integer, one eventually encountered an iterate = 1 (mod 4). - Jeff Lagarias, Sep 23, 2002.
Partial sums of 0,2,1,2,1,2,1,2,1.... - Paul Barry (pbarry(AT)wit.ie), Aug 18 2007
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REFERENCES
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L. Flatto, Z-numbers and beta-transformations, in Symbolic dynamics and its applications (New Haven, CT, 1991), 181-201, Contemp. Math., 135, Amer. Math. Soc., Providence, RI, 1992.
K. Mahler, An unsolved problem on the powers of 3/2, J. Austral. Math. Soc. 8 1968 313-321.
Sabinin, P. and Stone, M. G. ``Transforming n-gons by Folding the Plane.'' Amer. Math. Monthly 102, 620-627, 1995.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1002
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = 3n/2 if n even or (3n+1)/2 if n odd.
If u(1)=0, u(n)=n+floor(u(n-1)/3), then a(n-1)=u(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 26 2002
G.f.: x(x+2)/(1-x)^2/(1+x). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 13 2002
a(n) = 3*floor(n/2) + 2*(n mod 2) = A032766(n)+A000035(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Apr 04 2005
a(n)=(6n+1)/4-(-1)^n/4; a(n)=sum{k=0..n-1, 1+(-1)^(k/2)*cos(k*pi/2)}; - Paul Barry (pbarry(AT)wit.ie), Aug 18 2007
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MAPLE
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a[0]:=0:a[1]:=2:for n from 2 to 100 do a[n]:=a[n-2]+3 od: seq(a[n], n=0..71); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
with (combinat):seq(count(Partition((3*n+1)), size=2), n=0..71); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 28 2008
seq(add(irem(2^k, 3), k=1..n), n=0..71); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 20 2008
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CROSSREFS
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Cf. A063574.
Cf. A001651, A032766, A035361, A132462.
Sequence in context: A061054 A061723 A045506 this_sequence A052490 A117672 A139364
Adjacent sequences: A007491 A007492 A007493 this_sequence A007495 A007496 A007497
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KEYWORD
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nonn,easy
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AUTHOR
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Christopher Lam Cham Kee (Topher(AT)CyberDude.Com)
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