A094091 a(1) = 0; for n>0, a(n) = smaller of 0 and 1 such that we avoid the property that, for some i and j in the range S = 2 <= i < j <= n/2, a(i) ... a(2i) is a subsequence of a(j) ... a(2j).

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0

Offset: 1

Author

N. J. A. Sloane, May 02 2004

Keywords

• nonn
• fini
• full
• easy

Comments

A greedy version of A093383 and A093384.

This is a finite sequence of length 23 (necessarily <= A093382(2) = 31).

For S >= 1 define a sequence by a(1) = 0; for n>0, a(n) = smaller of 0 and 1 such that we avoid the property that, for some i and j in the range S <= i < j <= n/2, a(i) ... a(2i) is a subsequence of a(j) ... a(2j). The present sequence is the case S=2. For S=1 we get a sequence of length 3, namely 0,0,0, and A096094, A106197 are the cases S=3 and S=4. A093382(S) gives an upper bound on their lengths.

Examples

			After a(1) = a(2) = a(3) = a(4) = 0 we must have a(5) = 1, or else we would have a(2)a(3)a(4) = 000 as a subsequence of a(3)a(4)a(5)a(6) = 000a(6).
		

Links

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

Crossrefs

Cf. A093382, A093383, A093384, A096094, A106197.

Extensions

The remaining terms, a(17)-a(23), were sent by Joshua Zucker, Jul 23 2006