A214212 Number of right special factors of length n in the Thue-Morse sequence A010060.

1, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset

0,2

References

Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

S. Brlek, Enumeration of factors in the Thue-Morse word, Discrete Applied Math. 24 (1989), 83-96.

A. de Luca and S. Varricchio, Some combinatorial properties of the Thue-Morse sequence and a problem in semigroups, Theoret. Comput. Sci. 63 (1989), 333-348.

Formula

A005942(n+1) - A005942(n). - Michel Dekking, Sep 28 2020

Maple

ph:=proc(n) option remember;
if n=2 then 2 elif n<=3 then n+1 else if n mod 2 = 0 then ph(n/2) else ph((n+1)/2); fi;
fi; end;

Mathematica

ph[n_] := ph[n] = If[n == 2, 2, If[n <= 3, n+1, If[Mod[n, 2] == 0, ph[n/2], ph[(n+1)/2]]]];
ph /@ Range[0, 120] (* Jean-François Alcover, Jun 18 2020, after Maple *)

Crossrefs

Cf. A010060, A005942, A212214.

Sequence in context: A152858 A091248 A082991 * A100008 A102763 A054844

Adjacent sequences: A214209 A214210 A214211 * A214213 A214214 A214215

Keyword

nonn

Author

N. J. A. Sloane, Jul 10 2012

Extensions

Name clarified by Michel Dekking, Sep 28 2020

Status

approved