%I M3209 #20 Mar 06 2016 12:38:30
%S 4,3,3,11,35,395,13859,5474699,75873867299,415386585433442699,
%T 31516986660961757816520267299,
%U 13091733472248265157675672660811061946713442699,412611989213715130181341760777978491100613491478334525377331427960520267299
%N Knopfmacher expansion of 2/3: a(n+1) = a(n-1)(a(n)+1)-1.
%D A. Knopfmacher, ``Rational numbers with predictable Engel product expansions,'' in G. E. Bergum et al., eds., Applications of Fibonacci Numbers. Vol. 5, pp. 421-427.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A007568/b007568.txt">Table of n, a(n) for n = 0..17</a>
%H <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%F a(n) ~ c^(phi^n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio and c = 1.705023526853159146712304952... . - _Vaclav Kotesovec_, Mar 06 2016
%t t={1,3};Do[AppendTo[t,(t[[-1]]+1)*t[[-2]]-1],{n,11}];t[[1]]=4;t (* _Vladimir Joseph Stephan Orlovsky_, Jan 28 2012 *)
%t Flatten[{4, RecurrenceTable[{a[n+1] == a[n-1]*(a[n] + 1) - 1, a[1] == 3, a[2] == 3}, a, {n, 1, 12}]}] (* _Vaclav Kotesovec_, Mar 06 2016 *)
%K nonn
%O 0,1
%A _N. J. A. Sloane_, _Jeffrey Shallit_