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A007494
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Congruent to 0 or 2 mod 3.
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30
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
A145389(a(n)) <> 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 10 2008]
a(n) = A002943(n) - A173511(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 20 2010]
a(n) = numbers k such that antiharmonic mean of the first k positive integers is not integer. A169609(a(n-1)) = 3. See A146535 and A169609. Complement of A016777. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), May 28 2010]
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REFERENCES
| 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.
A. Mader, The Use of Experimental Mathematics in the Classroom, http://www.model.u-szeged.hu/etc/edoc/imp/AMader/AMader.pdf
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
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1002
Eric Weisstein's World of Mathematics, Folding
Index to sequences with linear recurrences with constant coefficients, signature (1,1,-1)
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FORMULA
| a(n) = 3*n/2 if n even, otherwise (3*n+1)/2.
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)gmail.com), Apr 04 2005
a(n)=(6*n+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
a(n)=3*n-a(n-1)-1 (with a(0)=0) [From Vincenzo Librandi, Nov 18 2010]
a(n)=Sum_k>=0 {A030308(n,k)*A042950(k)}. - From DELEHAM Philippe, Oct 17 2011.
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MAPLE
| 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
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MATHEMATICA
| sn=sd=s=0; lst={}; Do[a=n^2+n; b=n^2-n; c=a/b; sd+=Denominator[c]; sn+=Numerator[c]; AppendTo[lst, s=sn-sd], {n, 2, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 20 2009]
Flatten[{#, #+2}&/@(3Range[0, 40])] (* From Harvey P. Dale, May 15 2011 *)
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PROG
| (PARI) a(n)=n+(n+1)>>1 \\ Charles R Greathouse IV, Jul 25 2011
(MAGMA) [(6*n+1)/4-(-1)^n/4: n in [0..80]]; // Vincenzo Librandi, Aug 20 2011
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CROSSREFS
| Cf. A063574.
Cf. A001651, A032766, A035361, A132462.
Complement of A016777. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 10 2008]
Sequence in context: A061723 A195123 A045506 * A052490 A117672 A194383
Adjacent sequences: A007491 A007492 A007493 * A007495 A007496 A007497
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KEYWORD
| nonn,easy
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AUTHOR
| Christopher Lam Cham Kee (Topher(AT)CyberDude.Com)
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