# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a014709 Showing 1-1 of 1 %I A014709 #38 May 26 2024 16:05:12 %S A014709 1,1,2,1,1,2,2,1,1,1,2,2,1,2,2,1,1,1,2,1,1,2,2,2,1,1,2,2,1,2,2,1,1,1, %T A014709 2,1,1,2,2,1,1,1,2,2,1,2,2,2,1,1,2,1,1,2,2,2,1,1,2,2,1,2,2,1,1,1,2,1, %U A014709 1,2,2,1,1,1,2,2,1,2,2,1,1,1 %N A014709 The regular paper-folding (or dragon curve) sequence. %C A014709 Over the alphabet {a,b} this is aabaabbaaabbabbaaabaabbbaabbabbaaaba... %C A014709 With offset 1, completely multiplicative modulo 3. - _Peter Munn_, Jun 20 2022 %D A014709 J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, pp. 155, 182. %D A014709 G. Melançon, Factorizing infinite words using Maple, MapleTech journal, vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36. %H A014709 Ivan Panchenko, Table of n, a(n) for n = 0..10000 %H A014709 Gabriele Fici and Luca Q. Zamboni, On the least number of palindromes contained in an infinite word, Theoretical Computer Science, Volume 481, 2013, pp. 1-8. See page 1. %H A014709 Index entries for sequences obtained by enumerating foldings %F A014709 Set a=1, b=2, 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 A014709 a(4n) = 1, a(4n+2) = 2, a(2n+1) = a(n). %F A014709 a(n) = (3-jacobi(-1,n+1))/2 (cf. A034947). - _N. J. A. Sloane_, Jul 27 2012 [index adjusted by _Peter Munn_, Jun 22 2022] %F A014709 a(n) = 1 + A065339(n+1) mod 2. - _Peter Munn_, Jun 20 2022 %t A014709 (3 - JacobiSymbol[-1, Range[100]])/2 (* _Paolo Xausa_, May 26 2024 *) %o A014709 (PARI) a(n)=if(n%2==0, 1+bitand(1,n\2), a(n\2) ); %o A014709 for(n=0,122,print1(a(n),", ")) %Y A014709 See A014577 for more references and more terms. %Y A014709 The following are all essentially the same sequence: A014577, A014707, A014709, A014710, A034947, A038189, A082410. - _N. J. A. Sloane_, Jul 27 2012 %Y A014709 Cf. A065339. %K A014709 nonn %O A014709 0,3 %A A014709 _N. J. A. Sloane_. # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE