%I #30 Apr 11 2016 08:39:46
%S 3,6,33,1086,1179393,1390967848446,1934791555410494424614913,
%T 3743418362887760317407541271559358491868341997566
%N a(0) = 3; thereafter, a(n) = a(n-1)^2 - 3.
%C This is to A001566 as 3 is to 2 (subtrahend). Unlike A001566, which begins with 4 consecutive primes, this sequence can never be prime after a(0) = 3, because the first two terms are both multiples of 3, hence all later terms are. This is the k = 3 row of the array A(k, 0) = 3, A(k, n) = A(k, n-1)^2 - k; and A001566 is the k = 2 row. A003096(n+1) is the k = 1 row.
%H Vincenzo Librandi, <a href="/A186750/b186750.txt">Table of n, a(n) for n = 0..11</a>
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F a(n) ~ c^(2^n), where c = 2.3959550115176494685408322564302422183669584045032057908382914927198090627... - _Vaclav Kotesovec_, Dec 18 2014
%t RecurrenceTable[{a[0] == 3, a[n] == a[n-1]^2 - 3}, a, {n, 0, 10}] (* _Vaclav Kotesovec_, Dec 18 2014 *)
%t Drop[Abs[NestList[#^2 - 3 &, 0, 9]], 1] (* _Alonso del Arte_, Apr 08 2016 *)
%Y Cf. A001566, A003096.
%K nonn,easy
%O 0,1
%A _Jonathan Vos Post_, Feb 26 2011