A330022 - OEIS

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A330022

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

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.