Search: id:A014577
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%I A014577
%S A014577 1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,
%T A014577 1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,1,
%U A014577 0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,1,0
%N A014577 The regular paper-folding (or dragon curve) sequence.
%C A014577 Can be computed by storing only one large integer. It is the complement 
               of the bit to the left of the least significant "1" in the binary 
               expansion of n. E.g. n = 4 = 100, so a(4) = complement of bit to 
               left of 1, = 1. - Bob Brown (bobb(AT)webaccess.net), Nov 28 2001
%C A014577 To construct the sequence : start from 1,(..),0,(..),1,(..),0,(..),1,
               (..),0,(..),1,(..),0,... and fill undefined places with the sequence 
               itself. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 08 2007
%C A014577 A014577 is a generator for A088748: begin A088748 with "1" then add 1 
               if A014577: (1, 1, 0, 1, 1,...) = 1; subtract 1 otherwise, getting 
               (1, 2, 3, 2,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 
               30 2009]
%D A014577 M. Gardner, Mathematical Magic Show. New York: Vintage, pp. 207-209 and 
               215-220, 1978.
%D A014577 G. Melancon, Factorizing infinite words using Maple, MapleTech journal, 
               vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36.
%H A014577 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>
%H A014577 J.-P. Allouche and M. Mendes France, <a href="http://www.lri.fr/~allouche/
               ">Automata and Automatic Sequences.</a>
%H A014577 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DragonCurve.html">Link to a section of The World of Mathematics.</
               a>
%H A014577 <a href="Sindx_Fo.html#fold">Index entries for sequences obtained by 
               enumerating foldings</a>
%F A014577 Set a=1, b=0, S(0)=a, S(n+1) = S(n)aF(S(n)), where F(x) reverses x and 
               then interchanges a and b; sequence is limit S(infinity).
%F A014577 a(4n) = 1, a(4n+2) = 0, a(2n+1) = a(n). a(n) = 1 - A014707(n) = 2 - A014709(n) 
               = A014710(n) - 1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 
               03 2003
%Y A014577 See A014707, A014709, A014710 for other versions.
%Y A014577 Cf. A038189, A082410, A059125, A065339.
%Y A014577 A082410(n+2)=a(n).
%Y A014577 A088748 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 30 2009]
%Y A014577 Sequence in context: A080813 A100672 A079559 this_sequence A157926 A131377 
               A077049
%Y A014577 Adjacent sequences: A014574 A014575 A014576 this_sequence A014578 A014579 
               A014580
%K A014577 nonn,easy,nice
%O A014577 0,1
%A A014577 N. J. A. Sloane (njas(AT)research.att.com), Eric Weisstein (eric(AT)weisstein.com)
%E A014577 More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 03 2003

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