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A093914 a(1) = 1; for n > 1, a(n) = curling number of (b(1),...,b(n-1)), where b() = Thue-Morse sequence A010060 (with offset changed to 1). 4
1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The curling number of a finite string S = (s(1),...,s(n)) is the largest integer k such that S can be written as xy^k for strings x and y (where y has positive length).

From Andrey Zabolotskiy, Mar 03 2017: (Start)

The sequence consists of 1's and 2's only.

If 2^k>=n-1, then a(n+2^k)>=a(n).

The density of 1's seems to converge to 1/6.

(End)

LINKS

Andrey Zabolotskiy, Table of n, a(n) for n = 1..16384

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].

Index entries for sequences related to curling numbers

PROG

(Python)

p, tm, s = 8, 0, 1

for i in range(p):

    tm += (tm^((1<<s)-1))<<s

    s *= 2

print(1)

for i in range(1, 1<<p):

    a = any(((tm>>(i-j))&((1<<j)-1)) == ((tm>>(i-2*j))&((1<<j)-1)) for j in range(1, i//2+1))

    print(2 if a else 1)

# Andrey Zabolotskiy, Mar 03 2017

CROSSREFS

Cf. A090822, A010060.

Sequence in context: A206719 A240086 A305830 * A007061 A001817 A214973

Adjacent sequences:  A093911 A093912 A093913 * A093915 A093916 A093917

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 26 2004

STATUS

approved

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Last modified October 23 13:15 EDT 2018. Contains 316528 sequences. (Running on oeis4.)