A093382 - OEIS

A093382

a(n) = length k of longest binary sequence x(1) ... x(k) such that for no n <= i < j <= k/2 is x(i) ... x(2i) a subsequence of x(j) ... x(2j).

11, 31, 199

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OFFSET

1,1

COMMENTS

Doesn't the binary sequence 000010011001110011101010101010101010101100110 demonstrate that a(2) >= 45? - R. J. Mathar, Jul 29 2007 Answer: No - see the following comment.

The sequence of length 45 above does not satisfy the requirements of the definition: Subsequences are not required to be consecutive. Therefore it cannot show a(2) >= 45. In the sequence we find for i=2, j=3: x(i..2i) is 000; x(j..2j) is 001001; and 000 is a subsequence of 001001. - Don Reble, May 13 2008

a(4) >= 376843. - Bert Dobbelaere, May 25 2024

REFERENCES

a(1) - a(3) computed by R. Dougherty, who finds that a(4) >= 187205.

LINKS

Table of n, a(n) for n=1..3.

H. M. Friedman, Long finite sequences, J. Comb. Theory, A 95 (2001), 102-144.

EXAMPLE

a(1) = 11 from 01110000000.

CROSSREFS

See A093383-A093386 for illustrations of a(2) and a(3). Cf. A014221, A094091.

Sequence in context: A144727 A002535 A128337 * A098264 A023279 A068715

Adjacent sequences: A093379 A093380 A093381 * A093383 A093384 A093385

KEYWORD

nonn,bref,nice,more

AUTHOR

N. J. A. Sloane, Apr 29 2004

STATUS

approved