#Mathematica, <s>50</s> <s>48</s> 45 bytes

Mathematica generally sucks when it comes to code golf, but sometimes there's a built-in that makes things look really nice.

 f[n_]:=(a=2^IntegerExponent[n-1,2];1<n<1+a^2)

A test:

 Reap[Do[If[f[i],Sow[i]],{i,1,1000}][[2,1]]

 {3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 257, 289, 321, 353, 385, 417, 449, 481, 513, 545, 577, 609, 641, 673, 705, 737, 769, 801, 833, 865, 897, 929, 961, 993}