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A330022 Length of shortest binary string containing, as contiguous blocks, all palindromes of length n. 0

%I

%S 0,2,4,8,12,22,32

%N Length of shortest binary string containing, as contiguous blocks, all palindromes of length n.

%C Greedy supersequence algorithms give the upper bounds a(7) <= 60, a(8) <= 74, a(9) <= 142, a(10) <= 180, a(11) <= 344, a(12) <= 410, a(13) <= 798. Probably some of these are tight. The value for a(6) was computed by checking all 8! arrangements of the 8 palindromes of length 3, optimizing overlaps. Probably someone with more computing power could compute a(7) (resp., a(8)) by checking all 16! = 20922789888000 arrangements of the palindromes of length 7 (resp., 8).

%e The corresponding strings for 1 <= n <= 6 are:

%e 1: 01

%e 2: 0011

%e 3: 00010111

%e 4: 000011001111

%e 5: 0000010001010111011111

%e 6: 00000011001111000010010110111111

%Y Cf. A057148.

%K nonn,more

%O 0,2

%A _Jeffrey Shallit_, Nov 27 2019

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Last modified January 18 11:57 EST 2022. Contains 350455 sequences. (Running on oeis4.)