A138033 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.

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

Offset

1,6

Links

Table of n, a(n) for n=1..105.

Formula

Records occur at a(2^(i+1) - 2) = i.

For i>0, a(2^i + 1) = floor((i+1)/2).

Example

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.

Maple

(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;

Crossrefs

Cf. A000120.

Sequence in context: A156642 A360821 A155124 * A283876 A365663 A067754

Adjacent sequences: A138030 A138031 A138032 * A138034 A138035 A138036

Keyword

nonn,easy

Author

N. J. A. Sloane, May 30 2008

Status

approved