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A000324
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A nonlinear recurrence: a(n) = a(n-1)^2-4*a(n-1)+4 (for n>1).
(Formerly M3789 N1544)
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5
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OFFSET
| 0,2
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COMMENTS
| An infinite coprime sequence defined by recursion. - Michael Somos Mar 14 2004
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
A000058, A00215, A000289 and this sequence here can be represented as values of polynomials defined via P_0(z)= 1+z, P_{n+1}(z) = z+ prod_{i=0..n} P_i(z), with recurrences P_{n+1}(z) = (P_n(z))^2 -z*P_n(z) +z, n>=0. - Vladimir Shevelev (shevelev(AT)bgu.ac.il), Dec 08 2010
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REFERENCES
| S. W. Golomb, On certain nonlinear recurring sequences, Amer. Math. Monthly 70 (1963), 403-405.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.
S. Mustonen, On integer sequences with mutual k-residues
Index entries for sequences of form a(n+1)=a(n)^2 + ...
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FORMULA
| a(n)=L(2^n)+2, if n>0 where L() is Lucas sequence.
For n>=1, a(n) = 4+Prod{i=0,...,n-1} a(i). [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Dec 08 2010]
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PROG
| (PARI) a(n)=if(n<2, max(0, 1+4*n), a(n-1)^2-4*a(n-1)+4)
(PARI) a(n)=if(n<1, n==0, n=2^n; fibonacci(n+1)+fibonacci(n-1)+2)
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CROSSREFS
| a(n) = A001566(n-1)+2 (for n>0).
Cf. A000058.
Sequence in context: A100457 A080872 A173776 * A123817 A124421 A143554
Adjacent sequences: A000321 A000322 A000323 * A000325 A000326 A000327
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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