An (n,k)-sequence has been studied. A permutation a 1 ,a 2 ,...,a k n of 0,1,...,kn-1 is an (n,k)-sequence if a s + d -a s a t + d -a t (modn) whenever a s + d /n = a s /n and a t + d /n = a t /n for every s,t and d with 1=<s<t<t+d=<kn, where x is the integer part of x. We recall the ''prime construction'' of an (n,k)-sequence using a primitive root modulo p whenever kn+1=p is an odd prime. In this paper we show that (n,k)-sequences from the prime construction for a given p are ''essentially the same'' with each other regardless of the choice of primitive roots modulo p. Further, we study some interesting properties of (n,k)-sequences, especially those from prime construction. Finally, we present an updated table of essentially distinct (n,2)-sequences for n=<13. The smallest n for which the existence of an (n,2)-sequences is open now becomes 16.