一个递推数列中的素数

The primes in a recurrence sequence

设{an}n∞=1是满足递推关系a1=1,an+1=a2n+4an+2(n≥1)的数列.本文证明了:当n是偶数时,an仅当n=2时是素数.

Let { an}^∞n=1 be a sequence which satisfy a1 = 1,an＋1 = a^2n ＋ 4an ＋ 2 （ n ≥ 1 ）. In this paper we prove that a2 = 7 is a unique prime in { an}^∞n=1 with n is even.