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A056832
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All a(n) = 1 or 2; a(1) = 1; get next 2^k terms by repeating first 2^k terms and changing last element so sum of first 2^(k+1) terms is odd.
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6
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1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Fixed point of the morphism 1->12 and 2->11 (1 ->12 ->1211 ->12111212 ->..) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 31 2004
a(n) is multiplicative - Christian G. Bower (bowerc(AT)usa.net), Jun 03 2005
a(n) is the least k such that A010060(n-1+k)=1-A010060(n-1); the sequence {a(n+1)-1} is the characteristic sequence for A079523. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jun 22 2009]
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REFERENCES
| A. Hof, O. Knill and B. Simon, Singular continuous spectrum for palindromic Schroedinger operators, Commun. Math. Phys. 174 (1995), 149-159.
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FORMULA
| a(n)=((-1)^(n+1)*A002425(n)) modulo 3 - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 30 2003
a(1)=1, a(n)=1+{sum(i=1, n-1, a(i)*a(n-i)) mod 2} - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 16 2004
a(n) is multiplicative with a(2^e)=1+(1-(-1)^e)/2, a(p^e)=1 if p>2. - Michael Somos Jun 18 2005
[a(2^n+1) .. a(2^(n+1)-1)] = [a(1) .. a(2^n-1)]; a(2^(n+1))=3-a(2^n)
For n>0, a(n) = 2-A035263(n). - Benoit Cloitre, Nov 24, 2002
a(n)=2, if n-1 is in A079523; a(n)=1 otherwise. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jun 22 2009]
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EXAMPLE
| 1 -> 1,2 -> 1,2,1,1 -> 1,2,1,1,1,2,1,2 -> 1,2,1,1,1,2,1,2,1,2,1,1,1,2,1,1
1 el 2 elts 4 elements .. 8 elements ....... 16 elements
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MATHEMATICA
| Nest[ Function[l, {Flatten[(l /. {1 -> {1, 2}, 2 -> {1, 1}})]}], {1}, 7] (from Robert G. Wilson v Mar 03 2005)
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PROG
| (PARI) a(n)=numerator(2/n*(4^n-1)*bernfrac(2*n))%3
(PARI) a(n)=if(n<1, 0, valuation(n, 2)%2+1) /* Michael Somos Jun 18 2005 */
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CROSSREFS
| Sequence in context: A133162 A079806 A045887 * A105931 A173751 A126864
Adjacent sequences: A056829 A056830 A056831 * A056833 A056834 A056835
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KEYWORD
| easy,nonn,nice,mult
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AUTHOR
| Jonas Wallgren (jonwa(AT)ida.liu.se), Aug 30 2000
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