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A330022
Length of shortest binary string containing, as contiguous blocks, all palindromes of length n.
0
0, 2, 4, 8, 12, 22, 32
OFFSET
0,2
COMMENTS
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).
EXAMPLE
The corresponding strings for 1 <= n <= 6 are:
1: 01
2: 0011
3: 00010111
4: 000011001111
5: 0000010001010111011111
6: 00000011001111000010010110111111
CROSSREFS
Cf. A057148.
Sequence in context: A103787 A365076 A327480 * A362261 A032473 A084422
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Nov 27 2019
STATUS
approved