0,2

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]

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.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1002

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

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)gmail.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

Except for the first term, if a(1)=2, a(2)=3; a(n)=a(n-1)+1 (n even); a(n)=a(n-1)+2 (n odd) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 10 2009]

a(n)=3*n-a(n-1)-4 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]

For n=2, a(2)=3*2-0-4=2; n=3, a(3)=3*3-2-4=3; n=4, a(4)=3*4-3-4=5 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]

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

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]

Cf. A063574.

Cf. A001651, A032766, A035361, A132462.

Complement of A016777. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 10 2008]

Sequence in context: A061054 A061723 A045506 this_sequence A052490 A117672 A139364

Adjacent sequences: A007491 A007492 A007493 this_sequence A007495 A007496 A007497

nonn,easy,new

Christopher Lam Cham Kee (Topher(AT)CyberDude.Com)