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A014709 The regular paper-folding (or dragon curve) sequence. 8
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...

REFERENCES

J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, pp. 155, 182.

G. Melancon, Factorizing infinite words using Maple, MapleTech journal, vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..10000

Gabriele Fici, 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.

Index entries for sequences obtained by enumerating foldings

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))/2 (cf. A034947). - N. J. A. Sloane, Jul 27 2012

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

Sequence in context: A037826 A079882 A317335 * A278161 A069258 A273134

Adjacent sequences:  A014706 A014707 A014708 * A014710 A014711 A014712

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 19 16:08 EDT 2019. Contains 328223 sequences. (Running on oeis4.)