

A304681


Smallest odd positive integer t such that the prefix of length tn of the ThueMorse sequence (A010060) is an nantipower.


1



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
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OFFSET

1,3


COMMENTS

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


REFERENCES

Gabriele Fici, Antonio Restivo, Manuel Silva, and Luca Q. Zamboni, Antipowers in infinite words, Journal of Combinatorial Theory, Series A 157 (2018), 109119.


LINKS

Table of n, a(n) for n=1..79.
Colin Defant, AntiPower Prefixes of the ThueMorse 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 3antipowers, 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



