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a(0) = 3; thereafter, a(n) = a(n-1)^2 - 4.
1

%I #15 Nov 21 2013 12:50:08

%S 3,5,21,437,190965,36467631221,1329888126870853950837,

%T 1768602429992068534155014726612412013000565

%N a(0) = 3; thereafter, a(n) = a(n-1)^2 - 4.

%C This is to A001566 as 4 is to 2 (subtrahend). This is the k=4 row of the array A[k,0] = 3, A[k,n] = A[k,n-1]^2 - k; A186750 is the k=3 row; and A001566 is the k=2 row. A003096(n+1) is the k=1 row.

%e a(1) = a(0)^2 - 4 = 3^2 - 4 = 5, which is, like a(0), a prime.

%t NestList[#^2-4&,3,10] (* _Harvey P. Dale_, Mar 14 2011 *)

%Y Cf. A001566, A003096, A186750.

%K nonn,easy

%O 0,1

%A _Jonathan Vos Post_, Feb 26 2011