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A003842
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The infinite Fibonacci word (start with 2, apply 2->1, 1->12, take limit).
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15
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1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Fixed point of the morphism 1->12, 2->1, starting from a(1) = 2.
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REFERENCES
| E. Bombieri and J. Taylor, Which distribution of matter diffracts? An initial investigation, in International Workshop on Aperiodic Crystals (Les Houches, 1986), J. de Physique, Colloq. C3, 47 (1986), C3-19 to C3-28.
J. Grytczuk, Infinite semi-similar words, Discrete Math. 161 (1996), 133-141.
A. Hof, O. Knill and B. Simon, Singular continuous spectrum for palindromic Schroedinger operators, Commun. Math. Phys. 174 (1995), 149-159.
J. C. Lagarias, Number Theory and Dynamical Systems, pp. 35-72 of S. A. Burr, ed., The Unreasonable Effectiveness of Number Theory, Proc. Sympos. Appl. Math., 46 (1992). Amer. Math. Soc.
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.
F. Mignosi and L. Q. Zamboni, On the number of Arnoux-Rauzy words, Acta Arith. 101 (2002), 121-129.
P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
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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)=2, S(1)=1, S(n)=S(n-1)S(n-2); iterate. Sequence is S(infinity).
a(n-1)=n-floor(phi*floor(n/phi)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 28 2005
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MATHEMATICA
| Nest[ Flatten[ # /. {1 -> {1, 2}, 2 -> {1}}] &, {1}, 10] (from Robert G. Wilson v Mar 04 2005)
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CROSSREFS
| A003849 is the standard form of this sequence. This is the 2, 1 version. See also A014675, A005614, A001468.
Sequence in context: A131774 A078316 A055443 * A095771 A007421 A103921
Adjacent sequences: A003839 A003840 A003841 * A003843 A003844 A003845
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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