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%I #9 Apr 09 2014 10:13:02
%S 2,3,7,23,187,4643,898567,4192705463,3768229999719547,
%T 15799096080675502645110083,59534627833852486970959777827956950667527,
%U 940593305274293766389990332525291876515204489479064901503485974103
%N a(1) = 2, a(2) = 3, a(n+2) = a(n)*(a(n)+a(n+1)) - a(n+1).
%C Every term is coprime to every other term.
%C The next term has 107 digits.
%F a(n+2) = -a(n+1) + 5*product{k=1 to n} a(k)
%F Comments on asymptotics from Paul D. Hanna, Feb 05 2005:
%F Limit_{n->inf} log(a(n+1))/log(a(n)) = (sqrt(5)+1)/2 = 1.6180339887...
%F Limit_{n->inf} log(a(n))/((sqrt(5)+1)/2)^n = 0.471775871...
%F Limit_{n->inf} fraction( a(2n+2)/a(2n+1) ) = 0.9963258537736462872363456738414777019251922501451462595067...
%F Limit_{n->inf} fraction( a(2n+1)/a(2n) ) = 0.5781727423883458291832179527899399497969420087427440931499...
%t RecurrenceTable[{a[1]==2,a[2]==3,a[n]==a[n-2](a[n-2]+a[n-1])- a[n-1]}, a,{n,12}] (* _Harvey P. Dale_, Apr 23 2011 *)
%K easy,nonn
%O 1,1
%A _Leroy Quet_, Feb 05 2005
%E More terms from Paul D. Hanna, Feb 05 2005
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