A304681 Smallest odd positive integer t such that the prefix of length tn of the Thue-Morse sequence (A010060) is an n-antipower.

1, 1, 5, 5, 5, 5, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 25, 25, 29, 29, 29, 29, 35, 35, 35, 35, 39, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 49, 49, 49, 49, 49, 49, 49, 49, 57, 57, 57, 57, 57, 57, 57, 57, 57, 61, 61, 61, 61, 61, 61, 61, 61, 61, 91, 91, 95, 95, 95, 95

Offset

1,3

Comments

A word of length tn is an n-antipower if all n consecutive blocks of length t are distinct.

References

Gabriele Fici, Antonio Restivo, Manuel Silva, and Luca Q. Zamboni, Anti-powers in infinite words, Journal of Combinatorial Theory, Series A 157 (2018), 109-119.

Links

Table of n, a(n) for n=1..79.

Colin Defant, Anti-Power Prefixes of the Thue-Morse Word, Electronic J. Combinatorics 24 (1) (2017), Paper #P1.32.

Example

For n = 3, the prefixes (0)(1)(1) and (011)(010)(011) are not 3-antipowers, but the prefix (01101)(00110)(01011) is.

Crossrefs

Cf. A010060, A304682.

Sequence in context: A293982 A071577 A003870 * A076407 A134701 A291655

Adjacent sequences: A304678 A304679 A304680 * A304682 A304683 A304684

Keyword

nonn

Author

Jeffrey Shallit, May 16 2018

Status

approved