%I A000289 M3316 N1333
%S A000289 1,4,7,31,871,756031,571580604871,326704387862983487112031,
%T A000289 106735757048926752040856495274871386126283608871
%N A000289 A nonlinear recurrence: a(n) = a(n-1)^2-3*a(n-1)+3 (for n>1).
%C A000289 An infinite coprime sequence defined by recursion. - Michael Somos Mar 
               14 2004
%C A000289 This is the special case k=3 of sequences with exact mutual k-residues. 
               In general, a(1)=k+1 and a(n)=min{m | m>a(n-1), mod(m,a(i))=k, i=1,
               ...,n-1}. k=1 gives Sylvester's sequence A000058 and k=2 Fermat sequence 
               A000215. - Seppo Mustonen (seppo.mustonen(AT)helsinki.fi), Sep 4 
               2005
%D A000289 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000289 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000289 S. W. Golomb, On certain nonlinear recurring sequences, Amer. Math. Monthly 
               70 (1963), 403-405.
%H A000289 A. V. Aho and N. J. A. Sloane, <a href="http://www.research.att.com/~njas/
               doc/doubly.html">Some doubly exponential sequences</a>, Fib. Quart., 
               11 (1973), 429-437.
%H A000289 <a href="Sindx_Aa.html#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 
               + ...</a>
%H A000289 S. Mustonen, <a href="http://www.survo.fi/papers/resseq.pdf">On integer 
               sequences with mutual k-residues</a>
%F A000289 a(n)=ceiling(c^(2^n))+1 where c=1.526526457021345220425447875332... - 
               Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 29 2002
%o A000289 (PARI) a(n)=if(n<2,max(0,1+3*n),a(n-1)^2-3*a(n-1)+3)
%Y A000289 a(n) = A005267(n)+2 (for n>0).
%Y A000289 Cf. A000058.
%Y A000289 Sequence in context: A102666 A123801 A156228 this_sequence A149089 A004031 
               A153062
%Y A000289 Adjacent sequences: A000286 A000287 A000288 this_sequence A000290 A000291 
               A000292
%K A000289 nonn,easy
%O A000289 0,2
%A A000289 N. J. A. Sloane (njas(AT)research.att.com).