|
%I #3 Mar 30 2012 16:50:48
%S 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,
%T 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,
%U 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
%N 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.
%F Records occur at a(2^(i+1) - 2) = i.
%F For i>0, a(2^i + 1) = floor((i+1)/2).
%e Suppose n=8. We consider:
%e i=1, min{wt(1), wt(7)} = min{1,3} = 1,
%e i=2, min{wt(2), wt(6)} = min{1,2} = 1,
%e i=3, min{wt(3), wt(5)} = min{2,2} = 2,
%e i=4, min{wt(4), wt(4)} = min{1,1} = 1,
%e and the maximal value is 2, so a(8) = 2.
%p (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;
%Y Cf. A000120.
%K nonn,easy
%O 1,6
%A _N. J. A. Sloane_, May 30 2008
|
