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Search: id:A000289
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| A000289 |
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A nonlinear recurrence: a(n) = a(n-1)^2-3*a(n-1)+3 (for n>1).
(Formerly M3316 N1333)
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+0
6
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| 1, 4, 7, 31, 871, 756031, 571580604871, 326704387862983487112031, 106735757048926752040856495274871386126283608871
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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An infinite coprime sequence defined by recursion. - Michael Somos Mar 14 2004
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
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. W. Golomb, On certain nonlinear recurring sequences, Amer. Math. Monthly 70 (1963), 403-405.
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LINKS
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A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.
Index entries for sequences of form a(n+1)=a(n)^2 + ...
S. Mustonen, On integer sequences with mutual k-residues
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FORMULA
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a(n)=ceiling(c^(2^n))+1 where c=1.526526457021345220425447875332... - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 29 2002
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PROGRAM
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(PARI) a(n)=if(n<2, max(0, 1+3*n), a(n-1)^2-3*a(n-1)+3)
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CROSSREFS
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a(n) = A005267(n)+2 (for n>0).
Cf. A000058.
Sequence in context: A102666 A123801 A156228 this_sequence A149089 A004031 A153062
Adjacent sequences: A000286 A000287 A000288 this_sequence A000290 A000291 A000292
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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