A186437 - OEIS

%I #13 Feb 04 2015 23:25:23

%S 0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,3,4,4,4,4,4,4,4,4,5,5,5,

%T 5,5,5,5,4,5,5,5,4,5,5,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5

%N Maximal number of squarings in an evaluation scheme for x^n achieving the minimal number of operations.

%C a(n) is also the maximal number of doublings in a shortest addition chain for n.

%F We have a(n) = floor(log_2(n)) for all n ≤ 60 except 23, 39, 43 and 46.

%e For n=5, we can evaluate x^5 using only 3 operations in 2 ways:

%e   x^2 = (x)^2; x^3 = x * x^2; x^5 = x^2 * x^3

%e   x^2 = (x)^2; x^4 = (x^2)^2; x^5 = x * x^4

%e The second way achieves the maximal number of doublings, which is a(5) = 2.

%Y Cf A003313.

%K nonn

%O 1,4

%A Laurent Thévenoux and _Christophe Mouilleron_, Feb 23 2011