

A089215


ThueMorse sequence on the integers.


0



1, 2, 3, 2, 4, 3, 2, 3, 5, 4, 3, 4, 2, 3, 4, 3, 6, 5, 4, 5, 3, 4, 5, 4, 2, 3, 4, 3, 5, 4, 3, 4, 7, 6, 5, 6, 4, 5, 6, 5, 3, 4, 5, 4, 6, 5, 4, 5, 2, 3, 4, 3, 5, 4, 3, 4, 6, 5, 4, 5, 3, 4, 5, 4, 8, 7, 6, 7, 5, 6, 7, 6, 4, 5, 6, 5, 7, 6, 5, 6, 3, 4, 5, 4, 6, 5, 4, 5, 7, 6, 5, 6, 4, 5, 6, 5, 2, 3, 4, 3, 5, 4, 3, 4, 6
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OFFSET

1,2


COMMENTS

S(1)={1,2} then M(1)=4 and S'(1)={41,42}={3,2}. So S(2)={1,2,3,2}. M(2)=5 so S(3)={1,2,3,2}{51,52,53,52} and sequence begins 1,2,3,2,4,3,2,3,..


LINKS

Table of n, a(n) for n=1..105.


FORMULA

sum(k=1, n, a(k)) is asymptotic to C*n*log(n) with C=0.8....


EXAMPLE

Sequence is S(infinity) where S(1)={1,2} and S(n+1)=S(n)S'(n) where S'(n) is obtained from S(n) by substituting an element x of S(n) with M(n)x where M(n)=2+Max(S(n)}. ThueMorse sequence on alphabet {1,2}is constructed as follows: S(1)={1,2} and S(n+1)=S(n)S'(n) where S'(n) is obtained from S(n) by substituting an element x of S(n) with 3x


CROSSREFS

Cf. A001285.
Sequence in context: A288535 A105117 A100876 * A238766 A325239 A328739
Adjacent sequences: A089212 A089213 A089214 * A089216 A089217 A089218


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Dec 10 2003


STATUS

approved



