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Lengths of successive runs of 1's in the Thue-Morse sequence A010060.
5

%I #17 Dec 19 2023 03:30:35

%S 2,1,2,1,2,1,1,2,2,1,2,1,2,2,1,1,2,1,2,1,2,1,1,2,2,1,1,2,1,2,1,2,2,1,

%T 2,1,2,1,1,2,2,1,2,1,2,2,1,1,2,1,2,1,2,2,1,2,1,2,1,1,2,2,1,1,2,1,2,1,

%U 2,1,1,2,2,1,2,1,2,2,1,1,2,1,2,1,2,1,1,2,2,1,1,2,1,2,1,2,2,1,2,1,2,1,1,2,2

%N Lengths of successive runs of 1's in the Thue-Morse sequence A010060.

%C Also lengths of successive runs of 0's in the Thue-Morse sequence A010059.

%C Also lengths of successive runs of 2's in the Thue-Morse sequence A001285.

%C A variant of A036577, suggested by p. 4421 of Grytczuk.

%H Ray Chandler, <a href="/A104248/b104248.txt">Table of n, a(n) for n=1..10922</a>

%H Jaroslaw Grytczuk, <a href="http://dx.doi.org/10.1016/j.disc.2007.08.039">Thue type problems for graphs, points and numbers</a>, Discrete Math., 308 (2008), 4419-4429.

%F a(n) = A026465(2n).

%e A010060 begins 011010011001011010010110011010011... so the runs of 1's have lengths 2 1 2 1 2 1 1 2 2 1 2 1 2 2 1 1 2 1 ...

%t Map[Length,Most[Split[ThueMorse[Range[500]]]][[;;;;2]]] (* _Paolo Xausa_, Dec 19 2023 *)

%Y Cf. A010060, A036577, A143331.

%Y Cf. A001285, A010059, A026465.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Aug 05 2008

%E Edited and extended by _Ray Chandler_, Aug 08 2008