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Search: id:A000324
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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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+0
4
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| 1, 5, 9, 49, 2209, 4870849, 23725150497409, 562882766124611619513723649, 316837008400094222150776738483768236006420971486980609
(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=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
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REFERENCES
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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)=L(2^n)+2, if n>0 where L() is Lucas sequence.
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PROGRAM
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(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
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a(n) = A001566(n-1)+2 (for n>0).
Cf. A000058.
Adjacent sequences: A000321 A000322 A000323 this_sequence A000325 A000326 A000327
Sequence in context: A105182 A100457 A080872 this_sequence A123817 A124421 A098097
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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