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A014709 The regular paper-folding (or dragon curve) sequence. 9
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, 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, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Over the alphabet {a,b} this is aabaabbaaabbabbaaabaabbbaabbabbaaaba...
With offset 1, completely multiplicative modulo 3. - Peter Munn, Jun 20 2022
REFERENCES
J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, pp. 155, 182.
G. Melançon, Factorizing infinite words using Maple, MapleTech journal, vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36.
LINKS
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.
FORMULA
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).
a(4n) = 1, a(4n+2) = 2, a(2n+1) = a(n).
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]
a(n) = 1 + A065339(n+1) mod 2. - Peter Munn, Jun 20 2022
PROG
(PARI) a(n)=if(n%2==0, 1+bitand(1, n\2), a(n\2) );
for(n=0, 122, print1(a(n), ", "))
CROSSREFS
See A014577 for more references and more terms.
The following are all essentially the same sequence: A014577, A014707, A014709, A014710, A034947, A038189, A082410. - N. J. A. Sloane, Jul 27 2012
Cf. A065339.
Sequence in context: A079882 A362415 A317335 * A278161 A069258 A273134
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 28 13:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)