1.Introduction
The persistence of a number is defined by an iterative process. d(n,b) is the product of digits, in base b, of n. Example: d(329,10)=3*2*9=54, d(54,10)=20, d(20,10)=0. The persistence p(n,b) is the smallest number of step you can nest the above function d to n, so that the last result has only 1 digit. Example: p(329,10)=3. We define pmax(b) to be the maximum reached by p(n,b) for all n. At the moment only pmax(1)=0 and pmax(2)=1 are known. For bigger bases there are only lower bounds. We like to increase some lower bounds. It is conjunctured that pmax(3)=3. The reason for that conjuncture is that 2^n, for n>15, has at most 1 zero in its 3-adic representation. This is checked up to n=500 (1994). The author has checked this for all n<1010. Additionaly the minimal numbers min(p,b) in base b which have persistence p were examined.
