A304683 - OEIS

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A304683

Number of odd positive integers t such that the prefix of length tn of the Thue-Morse sequence (A010060) is not an n-antipower.

0, 0, 2, 2, 2, 3, 5, 5, 6, 7, 7, 7, 7, 7, 8, 8, 9, 10, 12, 12, 13, 14, 14, 15, 15, 16, 17, 17, 18, 18, 18, 18, 22, 24, 25, 26, 27, 29, 30, 30, 30, 31, 32, 33, 33, 33, 33, 35, 35, 35, 35, 35, 35, 35, 35, 37, 37, 37, 37, 37, 37, 39, 39, 39, 44, 47, 52, 52, 54, 55, 57, 60, 63, 66, 68, 69, 69, 70, 70, 71, 72, 72

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OFFSET

1,3

COMMENTS

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

Defant proved that a(n) is finite for all n.

LINKS

Table of n, a(n) for n=1..82.

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

CROSSREFS

Cf. A010060.

Cf. A304682, which gives the largest odd integer with the property.