Search: id:A000324
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%I A000324 M3789 N1544
%S A000324 1,5,9,49,2209,4870849,23725150497409,562882766124611619513723649,
%T A000324 316837008400094222150776738483768236006420971486980609
%N A000324 A nonlinear recurrence: a(n) = a(n-1)^2-4*a(n-1)+4 (for n>1).
%C A000324 An infinite coprime sequence defined by recursion. - Michael Somos Mar 
               14 2004
%C A000324 This is the special case k=4 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 A000324 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000324 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000324 S. W. Golomb, On certain nonlinear recurring sequences, Amer. Math. Monthly 
               70 (1963), 403-405.
%H A000324 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 A000324 <a href="Sindx_Aa.html#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 
               + ...</a>
%H A000324 S. Mustonen, <a href="http://www.survo.fi/papers/resseq.pdf">On integer 
               sequences with mutual k-residues</a>
%F A000324 a(n)=L(2^n)+2, if n>0 where L() is Lucas sequence.
%o A000324 (PARI) a(n)=if(n<2,max(0,1+4*n),a(n-1)^2-4*a(n-1)+4)
%o A000324 (PARI) a(n)=if(n<1,n==0,n=2^n;fibonacci(n+1)+fibonacci(n-1)+2)
%Y A000324 a(n) = A001566(n-1)+2 (for n>0).
%Y A000324 Cf. A000058.
%Y A000324 Sequence in context: A105182 A100457 A080872 this_sequence A123817 A124421 
               A143554
%Y A000324 Adjacent sequences: A000321 A000322 A000323 this_sequence A000325 A000326 
               A000327
%K A000324 nonn,easy
%O A000324 0,2
%A A000324 N. J. A. Sloane (njas(AT)research.att.com).

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