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Search: id:A094091
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| A094091 |
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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). |
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+0
4
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| 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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H. M. Friedman, Long finite sequences, J. Comb. Theory, A 95 (2001), 102-144.
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EXAMPLE
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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).
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CROSSREFS
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Cf. A093382, A093383, A093384, A096094, A106197.
Sequence in context: A118685 A080343 A011664 this_sequence A080679 A144193 A011662
Adjacent sequences: A094088 A094089 A094090 this_sequence A094092 A094093 A094094
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KEYWORD
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nonn,fini,full,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 02 2004
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EXTENSIONS
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The remaining terms, a(17)-a(23), were sent by Joshua Zucker (joshua.zucker(AT)gmail.com), Jul 23 2006.
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