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A014709
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The regular paper-folding (or dragon curve) sequence.
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9
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1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1
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OFFSET
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0,3
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COMMENTS
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Over the alphabet {a,b} this is aabaabbaaabbabbaaabaabbbaabbabbaaaba...
With offset 1, completely multiplicative modulo 3. - Peter Munn, Jun 20 2022
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, pp. 155, 182.
G. Melançon, Factorizing infinite words using Maple, MapleTech journal, vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36.
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LINKS
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FORMULA
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Set a=1, b=2, S(0)=a, S(n+1) = S(n)aF(S(n)), where F(x) reverses x and then interchanges a and b; sequence is limit S(infinity).
a(4n) = 1, a(4n+2) = 2, a(2n+1) = a(n).
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PROG
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(PARI) a(n)=if(n%2==0, 1+bitand(1, n\2), a(n\2) );
for(n=0, 122, print1(a(n), ", "))
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CROSSREFS
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See A014577 for more references and more terms.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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