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

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

Offset: 0

Author

Jeffrey Shallit, Nov 27 2019

Keywords

• nonn
• more

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).

Examples

			The corresponding strings for 1 <= n <= 6 are:
1: 01
2: 0011
3: 00010111
4: 000011001111
5: 0000010001010111011111
6: 00000011001111000010010110111111
		

Crossrefs

Cf. A057148.