  For a prime p and nonnegative integers n,k, consider the set A_{n,k}^{(p)}={x
is in [0,1,...,n]: p^k||binom {n} {x}}. Let the expansion of n+1 in base p be:
n+1=alpha_{0} p^{\nu}+alpha_{1}p^{nu-1}+...+alpha_{nu}, where 0<=alpha_{i}<=
p-1,i=0,...,nu. Then the number n is called a binomial predictor in base p,if
|A_{n,k}^{(p)}|=alpha_{k}p^{nu-k},k=0,1,...,nu. We give a full description of
the binomial predictors in base p.
