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Search: id:A000034
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| A000034 |
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A simple periodic sequence.
(Formerly M0089)
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+0
18
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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
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
Hankel transform is [1,-3,0,0,0,0,0,0,0,...]. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 29 2007
a(n) = A134451(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2007
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REFERENCES
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Jozsef Beck, Combinatorial Games, Cambridge University Press, 2008
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LINKS
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Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors ..., J. Integer Seqs., Vol. 6, 2003.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 383
Wikipedia, Collatz conjecture
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FORMULA
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G.f.: (1+2*x)/(1-x^2).
a(n)=2^((1-(-1)^n)/2)=2^(ceiling(n/2)-floor(n/2)). - Paul Barry (pbarry(AT)wit.ie), Jun 03 2003
a(n) = {3 - (-1)^n}/2, or a(n)=1+(n mod 2)=3-a(n-1)=a(n-2)=a(-n).
a(n)=gcd(n-1, n+1) - Paul Barry (pbarry(AT)wit.ie), Sep 16 2004
a(n)= 2*(n mod 2) + [(n+1) mod 2] with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Sep 20 2006
Binomial transform of A123344, inverse binomial transform of A003945 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 04 2007
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
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MAPLE
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(1+2*x)/(1-x^2);
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MATHEMATICA
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a[n_] := If[OddQ[n], 2, 1]; Table[a[n], {n, 0, 90}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 17 2006
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PROGRAM
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(PARI) a(n)=1+n%2
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CROSSREFS
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Adjacent sequences: A000031 A000032 A000033 this_sequence A000035 A000036 A000037
Sequence in context: A111621 A022927 A063435 this_sequence A040001 A134451 A066788
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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