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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 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=0..6.

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: A027677 A103787 A327480 * A032473 A084422 A175841

Adjacent sequences:  A330019 A330020 A330021 * A330023 A330024 A330025

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Nov 27 2019

STATUS

approved

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Last modified November 27 12:00 EST 2021. Contains 349386 sequences. (Running on oeis4.)