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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.

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.

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

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 January 21 11:20 EST 2019. Contains 319353 sequences. (Running on oeis4.)