%I #3 Mar 30 2012 17:31:12
%S 0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,0,1,0,0,4,0,0,0,3,0,4,0,0,2,0,0,4,0,
%T 5,5,0,0,4,0,0,4,0,0,7,0,0,0,5,1,4,0,0,6,8,0,4,0,0,5,0,0,7,0,8,8,0,0,
%U 4,3,0,6,0,0,8,0,9,9,0,0,7,0,0,5,8,0,4,0,0,9,11,0,4,0,8,0,0,3,9,3,0,9,0,0
%N Difference between the maximum number of consecutive integers and the least number >1 of consecutive integers, the sum of which equals 2n.
%C a(n)=0 iff n=2^k.
%D Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 67.
%e a(18) = 1 because 3+4+5+6 = 5+6+7 = 18.
%t f[n_] := Block[{r = Ceiling[n/2]}, If[ IntegerQ[ Log[2, n]], 0, m = Range[r]; lst = Flatten[ Table[ m[[k]], {i, r}, {j, i + 1, r}, {k, i, j}], 1]; l = Length /@ lst[[ Flatten[ Position[ Plus @@@ lst, n]]]]; Max[l] - Min[l]]]; Table[ f[2n], {n, 105}]
%Y Cf. A104512, A104513, A104514, A104516.
%K nonn
%O 1,15
%A Alfred S. Posamentier (asp2(AT)juno.com) and _Robert G. Wilson v_, Feb 23 2005