%I A000034 M0089
%S A000034 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,
%T A000034 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,
%U A000034 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2
%N A000034 A simple periodic sequence.
%C A000034 Also continued fraction for (sqrt(3)+1)/2 (cf. A040001) and base 3 digital 
               root of n+1 (cf. A007089, A010888) - Henry Bottomley (se16(AT)btinternet.com), 
               Jul 05 2001
%C A000034 The sequence 1,-2,-1,2,1,-2,-1,2,... with g.f. (1-2x)/(1+x^2) has a(n)=cos(pi*n/
               2)-2sin(pi*n/2) - Paul Barry (pbarry(AT)wit.ie), Oct 18 2004
%C A000034 Hankel transform is [1,-3,0,0,0,0,0,0,0,...]. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Mar 29 2007
%C A000034 a(n) = A134451(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 27 2007
%C A000034 4/33=0,121212... [From Eric Desbiaux (moongerms(AT)wanadoo.fr), Nov 03 
               2008]
%D A000034 Jozsef Beck, Combinatorial Games, Cambridge University Press, 2008
%D A000034 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000034 Daniele A. Gewurz and Francesca Merola, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">Sequences realized as Parker vectors ...</
               a>, J. Integer Seqs., Vol. 6, 2003.
%H A000034 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=383">
               Encyclopedia of Combinatorial Structures 383</a>
%H A000034 Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">
               Collatz conjecture</a>
%H A000034 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A000034 G.f.: (1+2*x)/(1-x^2).
%F A000034 a(n)=2^((1-(-1)^n)/2)=2^(ceiling(n/2)-floor(n/2)). - Paul Barry (pbarry(AT)wit.ie), 
               Jun 03 2003
%F A000034 a(n) = {3 - (-1)^n}/2, or a(n)=1+(n mod 2)=3-a(n-1)=a(n-2)=a(-n).
%F A000034 a(n)=gcd(n-1, n+1) - Paul Barry (pbarry(AT)wit.ie), Sep 16 2004
%F A000034 a(n)= 2*(n mod 2) + [(n+1) mod 2] with n>=0 - Paolo P. Lava (ppl(AT)spl.at), 
               Sep 20 2006
%F A000034 Binomial transform of A123344, inverse binomial transform of A003945 
               . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 04 2007
%F A000034 a(n)=if(n=0,1,if(mod(a(n-1),2)=0,a(n-1)/2,(3*a(n-1)+1)/2)). See Collatz 
               conjecture. - Paul Barry (pbarry(AT)wit.ie), Mar 31 2008
%p A000034 (1+2*x)/(1-x^2);
%t A000034 a[n_] := If[OddQ[n], 2, 1]; Table[a[n], {n, 0, 90}] - Stefan Steinerberger 
               (stefan.steinerberger(AT)gmail.com), Apr 17 2006
%o A000034 (PARI) a(n)=1+n%2
%Y A000034 Sequence in context: A140195 A022927 A063435 this_sequence A040001 A134451 
               A160990
%Y A000034 Adjacent sequences: A000031 A000032 A000033 this_sequence A000035 A000036 
               A000037
%K A000034 nonn,easy
%O A000034 0,2
%A A000034 N. J. A. Sloane (njas(AT)research.att.com).