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%I #11 Aug 17 2017 03:01:43
%S 1,1,3,5,17,87,1481,128849,190825371,24587658227981,
%T 4691949003375676905953,115364038518117215020660724770070895,
%U 541282185550473269502054702460138578085934426170057537937
%N a(0)=1, a(1)=1, a(n) = a(n-1)*a(n-2) + 2.
%C Prime for n=2,3,4 (a Fermat prime each time); prime for n=6. When is the next prime in the sequence? Semiprime for a(5) = 87 = 3 * 29, a(10) = 127 * 36944480341540763039. a(11) has 36 digits and is the product of 6 primes. a(12) has 57 digits and is the product of 4 primes. a(13) has 92 digits and is the product of at least 4 primes: 123419 * 35173043 * 80-digit-composite, with the second-smallest prime divisor starting with the concatenation of a(2),a(3),a(4). - _Jonathan Vos Post_, Feb 28 2005
%e a(4)=17, a(5)=87, a(6) = 17*87 + 2 = 1481.
%p a[0]:=1: a[1]:=1: for n from 2 to 13 do a[n]:=a[n-1]*a[n-2]+2 od: seq(a[n],n=0..13); # _Emeric Deutsch_, Mar 08 2005
%K easy,nonn
%O 0,3
%A _Miklos Kristof_, Feb 28 2005
%E More terms from _Emeric Deutsch_, Mar 08 2005
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