一类递推数列中的素数

The Prim in a Type of Recurrence Sequence

设{a_n}~∞n=1是满足递推关系a1=1,a_(n+1)=a_n^2+2ka_n+k^2-k(n≥1)的数列。若k2+k+1为素数,当n是偶数时,当且仅当n=2时a_n是素数。

Let {a_n}~∞n=1 be a sequence which satisfies a1=1,an+1=a2n+2kan+k2-k(n≥1).Supposing k2+k+1 is prime, We prove k2+k+1 is a unique prime inan when n is even