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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
38
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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
4/33=0,121212... [From Eric Desbiaux (moongerms(AT)wanadoo.fr), Nov 03 2008]
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REFERENCES
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Jozsef Beck, Combinatorial Games, Cambridge University Press, 2008
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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
Index entries for sequences related to linear recurrences with constant coefficients
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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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Sequence in context: A140195 A022927 A063435 this_sequence A040001 A134451 A160990
Adjacent sequences: A000031 A000032 A000033 this_sequence A000035 A000036 A000037
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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