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Length of shortest string having n distinct letters and containing no 4-antipowers.
0

%I #11 Jun 19 2020 04:41:11

%S 1,2,3,5,6,10,16,52

%N Length of shortest string having n distinct letters and containing no 4-antipowers.

%C A 4-antipower consists of 4 consecutive blocks of the same length that are pairwise distinct. For example, 01021210 = (01)(02)(12)(10) is a 4-antipower.

%e Here are the lexicographically least examples for 1 <= n <= 8:

%e 1: 0

%e 2: 01

%e 3: 012

%e 4: 01123

%e 5: 012234

%e 6: 0121213345

%e 7: 0112333333334456

%e 8: 0112333333333333333333333333333333333334333333335567

%Y Cf. A275061.

%K nonn,more

%O 1,2

%A _Jeffrey Shallit_, Jun 14 2020