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

Offset: 1

Author

N. J. A. Sloane, Apr 29 2004

Keywords

• nonn
• bref
• nice
• more

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

Examples

			a(1) = 11 from 01110000000.
		

References

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

Links

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

Crossrefs

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