A268242 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A268242

Number of privileged factors of length n in Thue-Morse sequence A010060.

1, 2, 2, 2, 2, 0, 4, 0, 8, 0, 8, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 8, 0, 8, 0, 4, 0, 6, 0, 14, 0, 14, 0, 6, 0, 4, 0, 8, 0, 8, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

It appears that all terms except a(0) are even.

LINKS

Lars Blomberg, Table of n, a(n) for n = 0..10000

Jarkko Peltomäki, Privileged factors in the Thue-Morse word — a comparison of privileged words and palindromes, arXiv:1306.6768 [math.CO], 2013-2015 [Disc. Appl. Math., 193:187-199, 2015].

Jarkko Peltomäki, Privileged Words and Sturmian Words, Turku Centre for Computer Science, TUCS Dissertations No 214, August 2016.

Luke Schaeffer, Jeffrey Shallit, Closed, Palindromic, Rich, Privileged, Trapezoidal, and Balanced Words in Automatic Sequences, Electronic Journal of Combinatorics 23(1) (2016), #P1.25. Gives explicit formula for a(n).

CROSSREFS

Cf. A010060.