A306798 Starting position of first subword of length n of the Thue-Morse sequence (A010060) maximizing the number of unbordered conjugates (sequence A321162).

0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 7, 0, 16, 4, 0, 5, 1, 0, 2, 0, 0, 1, 16, 1, 5, 5, 0, 0, 33, 31, 0, 5, 1, 0, 6, 9, 0, 1, 7, 1, 9, 4, 0, 0, 1, 0, 31, 1, 5, 5, 0, 1, 9, 7, 0, 9, 1, 0, 7, 0, 64, 65, 0, 5, 1, 0, 18, 9, 0, 1, 7, 1, 9, 7, 0, 17, 1, 0, 21, 1

Offset

1,9

Comments

Here we are indexing the Thue-Morse sequence t starting at position 0, so the relevant subword is t[a(i)..a(i)+n-1].

A conjugate of a word x is a cyclic shift of x. A word w is bordered if it contains a nonempty prefix y, not equal to w, that is also a suffix.

References

D. Gabric and J. Shallit, Notes on unbordered conjugates, in preparation.

Links

Table of n, a(n) for n=1..84.

Crossrefs

Cf. A010060, A321162.

Sequence in context: A037188 A276847 A271231 * A086079 A296338 A133703

Adjacent sequences: A306795 A306796 A306797 * A306799 A306800 A306801

Keyword

nonn

Author

Jeffrey Shallit, Mar 11 2019

Status

approved