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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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15
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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; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| 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.
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7, p. 36.
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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LINKS
| T. D. Noe, Table of n, a(n) for n=0..10945 (20 iterations)
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FORMULA
| Define strings S(0)=1, S(1)=2, S(n)=S(n-1).S(n-2) for n>=2. Sequence is S(infinity).
a(n) = floor((n+2)*phi) - floor((n+1)*phi) = A000201(n+2)-A000201(n+1), phi =(1+ sqrt 5)/2.
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MAPLE
| Digits := 50: t := evalf( (1+sqrt(5))/2); A014675 := n->floor((n+2)*t)-floor((n+1)*t);
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MATHEMATICA
| Nest[ Flatten[ # /. {1 -> 2, 2 -> {2, 1}}] &, {1}, 11] (* Robert G. Wilson v *)
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CROSSREFS
| This is the 1, 2 version. The standard form is A003849. See also A005614.
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: A109925 A180227 A001468 * A107362 A166332 A022303
Adjacent sequences: A014672 A014673 A014674 * A014676 A014677 A014678
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected by N. J. A. Sloane (njas(AT)research.att.com), Nov 07, 2001
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