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A003096
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a(n) = a(n-1)^2 - 1.
(Formerly M0894)
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6
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OFFSET
| 0,1
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COMMENTS
| After a(0) = 2 and a(1) = 3, this can never be prime, since a(n) = (a(n-1)+1) * (a(n-1)-1). Yet each term is relatively prime to its successor. The initial value a(0) is arbitrary, however these properties hold for any integer a(0) > 1. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 06 2008
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REFERENCES
| R. K. Guy, How to factor a number, Proc. 5th Manitoba Conf. Numerical Math., Congress. Num. 16 (1975), 49-89.
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.
Index entries for sequences of form a(n+1)=a(n)^2 + ...
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FORMULA
| a(n-1)=ceiling(c^(2^n)) where c=1.2955535361865325413981559700593353... - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 29 2002
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MATHEMATICA
| a=2; lst={a}; Do[b=a^2-1; AppendTo[lst, b]; a=b, {n, 10}]; lst (*From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), 28 Dec 2010*)
NestList[#^2-1&, 2, 10] (* From Harvey P. Dale, Nov 06 2011 *)
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PROG
| (PARI) a(n)=if(n<1, 2*(n==0), a(n-1)^2-1)
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CROSSREFS
| Sequence in context: A160634 A072043 A095203 * A042815 A191353 A005008
Adjacent sequences: A003093 A003094 A003095 * A003097 A003098 A003099
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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