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A092334
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For S a finite string of numbers, let M(S) denote the maximal number among them. Let a(1)=1. For n>1, a(n) is the greatest k such that the string a(1)a(2)...a(n-1) can be written in the form [x][y_1][y_2]...[y_k] where each y_i is of positive (but not necessarily equal) length and M(y_i)=M(y_j) for all i,j.
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0
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1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 4, 3, 3, 3, 3, 4, 4, 5, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2
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OFFSET
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1,3
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COMMENTS
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Here multiplication denotes concatenation of strings. This is Gijswijt's sequence, A090822, except we count 'y' blocks as being equivalent as long as their maximal elements are identical.
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LINKS
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F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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J. Taylor (integersfan(AT)yahoo.com), Mar 17 2004
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STATUS
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approved
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