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Search: id:A071858
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| A071858 |
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(Number of 1's in binary expansion of n) mod 3. |
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+0
3
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| 0, 1, 1, 2, 1, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 1, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 0, 1, 1, 2, 2, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 0, 1, 1, 2, 2, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 0, 1, 1, 2, 0
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Ternary sequence which is a fixed point of the morphism 0 -> 01, 1 -> 12, 2 -> 20.
Sequence is T^(infty)(0) where T is the operator acting on any word on alphabet {0,1,2} by inserting 1 after 0, 2 after 1 and 0 after 2. For instance T(001)=010112, T(120)=122001. [From Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 02 2009]
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FORMULA
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Recurrence: a(2n) = a(n), a(2n+1) = (a(n)+1) mod 3.
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MATHEMATICA
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f[n_] := Mod[ Count[ IntegerDigits[n, 2], 1], 3]; Table[ f[n], {n, 0, 104}] (* Or *)
Nest[ Function[ l, {Flatten[(l /. {0 -> {0, 1}, 1 -> {1, 2}, 2 -> {2, 0}}) ]}], {0}, 7] (from Robert G. Wilson v Mar 03 2005)
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PROGRAM
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(PARI) for(n=1, 200, print1(sum(i=1, length(binary(n)), component(binary(n), i))%3, ", "))
(PARI) map(d)=if(d==2, [2, 0], if(d==1, [1, 2], [0, 1]))
{m=53; v=[]; w=[0]; while(v!=w, v=w; w=[]; for(n=1, min(m, length(v)), w=concat(w, map(v[n])))); for(n=1, 2*m, print1(v[n], ", "))} - Klaus Brockhaus, Jun 23 2004
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CROSSREFS
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Equals A010872(A000120(n)).
Cf. A010060, A001285, A010059, A048707, A096271, A100619.
Sequence in context: A038717 A073267 A159981 this_sequence A122864 A140084 A105937
Adjacent sequences: A071855 A071856 A071857 this_sequence A071859 A071860 A071861
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 09 2002
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EXTENSIONS
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Edited by Ralf Stephan, Dec 11 2004
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