Search: id:A014675
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%I A014675
%S A014675 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,
%T A014675 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,
%U A014675 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
%N A014675 The infinite Fibonacci word (start with 1, apply 1->2, 2->21, take limit).
%D A014675 M. Bunder and K. Tognetti, On the self matching properties of [j tau], 
               Discrete Math., 241 (2001), 139-151.
%D A014675 J. Grytczuk, Infinite semi-similar words, Discrete Math. 161 (1996), 
               133-141.
%D A014675 G. Melancon, Factorizing infinite words using Maple, MapleTech journal, 
               vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36.
%D A014675 G. Melancon, Lyndon factorization of sturmian words, Discr. Math., 210 
               (2000), 137-149.
%H A014675 T. D. Noe, <a href="b014675.txt">Table of n, a(n) for n=0..10945</a> 
               (20 iterations)
%F A014675 Define strings S(0)=1, S(1)=2, S(n)=S(n-1)S(n-2); iterate. Sequence is 
               S(infinity).
%F A014675 a(n) = [(n+1)*phi] - [n*phi], phi =(1+ sqrt 5)/2.
%p A014675 Digits := 50: t := evalf( (1+sqrt(5))/2); A014675 := n->floor((n+1)*t)-floor(n*t);
%t A014675 Nest[ Flatten[ # /. {1 -> 2, 2 -> {2, 1}}] &, {1}, 11] (* Robert G. Wilson 
               v *)
%Y A014675 This is the 1, 2 version. The standard form is A003849. See also A005614. 
               First differences of A000201.
%Y A014675 Cf. A082389.
%Y A014675 Differs from A025143 in many entries starting at entry 8. Same as A001468 
               if an initial 1 is added.
%Y A014675 Cf. A008351.
%Y A014675 Sequence in context: A080634 A109925 A001468 this_sequence A107362 A166332 
               A022303
%Y A014675 Adjacent sequences: A014672 A014673 A014674 this_sequence A014676 A014677 
               A014678
%K A014675 nonn,easy,nice
%O A014675 0,1
%A A014675 N. J. A. Sloane (njas(AT)research.att.com).
%E A014675 Corrected by N. J. A. Sloane (njas(AT)research.att.com), Nov 07, 2001

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