Representable Numbers with 1 Small Step Chains
            
   2* 2  @(p)+@(q)
            
legend:

1st column:  number of terms in sum (1-bits in binary representation)
2nd column:  a star indicates constructable by a star-chain
3rd column:  number of parameters for this family
          
p,q  are free variables for non negative integer values
@(.)  means  2^(.)
all 2-power exponents are strictly montonic decreasing ordered in the sum representation of each parametric family