本文推广了文[1]中自生数的概念。 定义。A_n是n位正整数。若存在大于1的正整数k,使得A_n的k次幂A_n~k的末n位数仍是A_n,则称A_n是一个n位自生数。否则就说A_n是非自生数。 显然,正整数A_n是n位自生数的充分必要条件是k∈N-{1}使得A_n~k-A_n 0(mod10~n)。可以看出,以上的k不是唯一的。若k=min{m|m∈N-{1},A_m~n-A_n 0(mod10~n),则我们还特别称A_n是k次n位自生数。约定当A_n This article generalizes the concept of self-generated number in [1]. definition. A_n is an n-bit positive integer. If there is a positive integer k greater than 1, such that the last n bits of A_n’s k power A_n~k are still A_n, A_n is said to be an n-bit self-generated number. Otherwise, say A_n is a non-self number. Obviously, a necessary and sufficient condition for the positive integer A_n to be an n-bit autogenous number is that k∈N-{1} makes A_n~k-A_n 0(mod10~n). It can be seen that the above k is not unique. If k=min{m|m∈N-{1}, A_m~n-A_n 0(mod10~n), we also specifically call A_n to be k times n-bit autogenous numbers. Conventions when A_n