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Search: id:A014675
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| A014675 |
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The infinite Fibonacci word (start with 1, apply 1->2, 2->21, take limit). |
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+0
13
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| 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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M. Bunder and K. Tognetti, On the self matching properties of [j tau], Discrete Math., 241 (2001), 139-151.
J. Grytczuk, Infinite semi-similar words, Discrete Math. 161 (1996), 133-141.
G. Melancon, Factorizing infinite words using Maple, MapleTech journal, vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36.
G. Melancon, Lyndon factorization of sturmian words, Discr. Math., 210 (2000), 137-149.
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FORMULA
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Define strings S(0)=1, S(1)=2, S(n)=S(n-1)S(n-2); iterate. Sequence is S(infinity).
a(n) = [(n+1)*phi] - [n*phi], phi =(1+ sqrt 5)/2.
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MAPLE
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Digits := 50: t := evalf( (1+sqrt(5))/2); A014675 := n->floor((n+1)*t)-floor(n*t);
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MATHEMATICA
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Nest[ Flatten[ # /. {1 -> 2, 2 -> {2, 1}}] &, {1}, 11] (* Robert G. Wilson v *)
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CROSSREFS
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This is the 1, 2 version. The standard form is A003849. See also A005614. First differences of A000201.
Cf. A082389.
Differs from A025143 in many entries starting at entry 8. Same as A001468 if an initial 1 is added.
Cf. A008351.
Sequence in context: A080634 A109925 A001468 this_sequence A107362 A022303 A113189
Adjacent sequences: A014672 A014673 A014674 this_sequence A014676 A014677 A014678
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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Corrected by njas, Nov 07, 2001
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