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Search: id:A138033
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| A138033 |
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a(n) = max_{ 1 <= i <= n-1 } min{ wt(i), wt(n-i) }, where wt() = A000120() is the binary weight function; a(1) = 0 by convention. |
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+0
1
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| 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 4, 4, 3, 3, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 5, 3, 3, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 5, 3, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 5, 5, 5, 3, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4
(list; graph; listen)
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OFFSET
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1,6
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FORMULA
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Records occur at a(2^(i+1) - 2) = i.
For i>0, a(2^i + 1) = floor((i+1)/2).
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EXAMPLE
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Suppose n=8. We consider:
i=1, min{wt(1), wt(7)} = min{1,3} = 1,
i=2, min{wt(2), wt(6)} = min{1,2} = 1,
i=3, min{wt(3), wt(5)} = min{2,2} = 2,
i=4, min{wt(4), wt(4)} = min{1,1} = 1,
and the maximal value is 2, so a(8) = 2.
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MAPLE
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(First load "wt" from A000120) f:=proc(n) local i, j, k; if n=1 then RETURN(0); fi; j:=0; for i from 1 to floor(n/2) do k := min( wt(i), wt(n-i) ); if k > j then j:=k; fi; od: RETURN(j); end;
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CROSSREFS
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Cf. A000120.
Sequence in context: A030547 A156642 A155124 this_sequence A067754 A025851 A125688
Adjacent sequences: A138030 A138031 A138032 this_sequence A138034 A138035 A138036
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 30 2008
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