3. Bounds on p_{max}(b)
p_{max}(1)=0 and p_{max}(2)=1 were mentioned in the introduction. For bigger bases there are only lower bounds. N.J.A. Sloane conjunctures that p_{max(b)} is finite. Now we examine the first few bases and the appropriate p_{max}(b)-values.

To strength the conjucture of N.J.A. Sloane, we conjucture that for every base b there is a m(b), so that all n>=m(b), without a 1 in the b-adic representation, yield to p(n,b)=2.