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A089215 Thue-Morse 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

S(1)={1,2} then M(1)=4 and S'(1)={4-1,4-2}={3,2}. So S(2)={1,2,3,2}. M(2)=5 so S(3)={1,2,3,2}{5-1,5-2,5-3,5-2} 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)}. Thue-Morse 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 3-x

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

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Last modified July 4 14:51 EDT 2020. Contains 335448 sequences. (Running on oeis4.)