

A093914


a(1) = 1; for n > 1, a(n) = curling number of (b(1),...,b(n1)), where b() = ThueMorse 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
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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>=n1, 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 SlowGrowing 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 SlowGrowing 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>>(ij))&((1<<j)1)) == ((tm>>(i2*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: A240086 A322306 A305830 * A007061 A001817 A214973
Adjacent sequences: A093911 A093912 A093913 * A093915 A093916 A093917


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, May 26 2004


STATUS

approved



